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+
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A note on the two variable Artin's conjecture
|
2024
|
Somnath Hazra
M. Ram Murty
Jyothsnaa Sivaraman
|
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+
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A simple proof of the Wiener–Ikehara Tauberian Theorem
|
2024
|
M. Ram Murty
Jagannath Sahoo
Akshaa Vatwani
|
|
+
PDF
|
The large sieve revisited
|
2024
|
M. Ram Murty
|
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+
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An all-purpose Erdös-Kac theorem
|
2023
|
M. Ram Murty
V. Kumar Murty
Sudhir Pujahari
|
|
+
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On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums
|
2023
|
Sneha Chaubey
Shivani Goel
M. Ram Murty
|
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+
PDF
|
Distribution of prime numbers
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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Arithmetic functions
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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Waring’s problem
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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Introduction to congruence arithmetic
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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An introduction to Waring’s problem
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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Exponential sums
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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Fundamental theorem for arithmetic
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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The circle method and the Goldbach conjectures
|
2023
|
M. Ram Murty
Kaneenika Sinha
|
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+
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On Hasse’s inequality
|
2023
|
M. Ram Murty
|
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+
PDF
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On Ihara’s conjectures for Euler–Kronecker constants
|
2023
|
Anup B. Dixit
M. Ram Murty
|
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+
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Irrationality of Zeros of the Digamma Function
|
2023
|
M. Ram Murty
|
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+
PDF
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A variant of the Hardy-Ramanujan theorem
|
2022
|
M. Ram Murty
V. Kumar Murty
|
|
+
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Graphs and Matrices
|
2022
|
Sebastian M. Cioabă
M. Ram Murty
|
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+
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A Second Course in Analysis
|
2022
|
M. Ram Murty
|
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+
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Expanders and Ramanujan Graphs
|
2022
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
PDF
|
Correction to: Graphs and Matrices
|
2022
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
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The Okada space and vanishing of ${L(1,{f})}$
|
2021
|
M. Ram Murty
Siddhi Pathak
|
|
+
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On the density of irreducible polynomials which generate k-free polynomials over function fields
|
2021
|
Seoyoung Kim
M. Ram Murty
|
|
+
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Mathematics of the Pandemic
|
2021
|
M. Ram Murty
V. Kumar Murty
|
|
+
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On the normal number of prime factors of sums of Fourier coefficients of eigenforms
|
2021
|
M. Ram Murty
V. Kumar Murty
Sudhir Pujahari
|
|
+
PDF
|
A localized Erdős-Kac theorem
|
2021
|
Anup B. Dixit
M. Ram Murty
|
|
+
|
Convolution of values of the Lerch zeta-function
|
2020
|
M. Ram Murty
Siddhi Pathak
|
|
+
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Artin's primitive root conjecture for function fields revisited
|
2020
|
Seoyoung Kim
M. Ram Murty
|
|
+
PDF
|
Class Numbers of Quadratic Fields
|
2020
|
Ajit Bhand
M. Ram Murty
|
|
+
|
The Central Limit Theorem in Algebra and Number Theory
|
2020
|
Arpita Kar
M. Ram Murty
|
|
+
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Central limit theorems for sums of quadratic characters, Hecke eigenforms, and elliptic curves
|
2019
|
M. Ram Murty
Neha Prabhu
|
|
+
PDF
|
Diophantine m-tuples with the property D(n)
|
2019
|
Riley Becker
M. Ram Murty
|
|
+
|
Cantor and infinity
|
2019
|
M. Ram Murty
Brandon Fodden
|
|
+
|
Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes
|
2019
|
M. Ram Murty
François Séguin
|
|
+
PDF
Chat
|
THE ERROR TERM IN THE SATO–TATE THEOREM OF BIRCH
|
2019
|
M. Ram Murty
Neha Prabhu
|
|
+
PDF
|
The Zeta Mahler measure of $(z^n − 1)/(z − 1)$
|
2019
|
Arunabha Biswas
M. Ram Murty
|
|
+
|
Smooth arithmetical sums over k-free integers
|
2019
|
Francesco Cellarosi
M. Ram Murty
|
|
+
|
A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences
|
2018
|
M. Ram Murty
François Séguin
C. L. Stewart
|
|
+
PDF
Chat
|
Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms
|
2018
|
Moni Kumari
M. Ram Murty
|
|
+
|
Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms
|
2018
|
Moni Kumari
M. Ram Murty
|
|
+
|
Transcendental numbers and special values of Dirichlet series
|
2018
|
M. Ram Murty
|
|
+
|
Transcendental sums related to the zeros of zeta functions
|
2018
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
A Smooth Selberg Sieve and Applications
|
2018
|
M. Ram Murty
Akshaa Vatwani
|
|
+
|
Overview of the Work of Kumar Murty
|
2018
|
Amir Akbary
Sanoli Gun
M. Ram Murty
|
|
+
PDF
Chat
|
TRANSCENDENTAL SUMS RELATED TO THE ZEROS OF ZETA FUNCTIONS
|
2018
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
PDF
Chat
|
Special values of derivatives of $L$-series and generalized Stieltjes constants
|
2018
|
M. Ram Murty
Siddhi Pathak
|
|
+
|
Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, II
|
2017
|
Giovanni Coppola
M. Ram Murty
|
|
+
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On the transcendence of certain Petersson inner products
|
2017
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Twin primes and the parity problem
|
2017
|
M. Ram Murty
Akshaa Vatwani
|
|
+
|
The analog of the Erdös distance problem in finite fields
|
2017
|
Sukumar Das Adhikari
Anirban Mukhopadhyay
M. Ram Murty
|
|
+
PDF
|
A higher rank Selberg sieve with an additive twist and applications
|
2017
|
M. Ram Murty
Akshaa Vatwani
|
|
+
|
On the number of special numbers
|
2017
|
Kevser Aktaş
M. Ram Murty
|
|
+
|
Finite order elements in the integral symplectic group
|
2017
|
Kumar Balasubramanian
M. Ram Murty
Karam Deo Shankhadhar
|
|
+
PDF
Chat
|
Bertrand’s postulate for number fields
|
2016
|
Thomas A. Hulse
M. Ram Murty
|
|
+
|
Finite Ramanujan expansions and shifted convolution sums of arithmetical functions
|
2016
|
Giovanni Coppola
M. Ram Murty
Biswajyoti Saha
|
|
+
PDF
|
Oscillations of coefficients of Dirichlet series attached to automorphic forms
|
2016
|
Jaban Meher
M. Ram Murty
|
|
+
|
Some remarks related to Maeda’s conjecture
|
2016
|
M. Ram Murty
Srinivas Kotyada
|
|
+
|
A Generalization of Euler's Theorem for <em>ζ</em>(2<em>k</em>)
|
2016
|
M. Ram Murty
Chester Weatherby
|
|
+
PDF
|
ON THE ASYMPTOTIC FORMULA FOR THE FOURIER COEFFICIENTS OF THE <b><i>j</i></b>-FUNCTION
|
2016
|
M. Ram Murty
Kannappan Sampath
|
|
+
|
Modular Forms of Level One
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
Jacobi’s q-series
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
Modular Forms of Higher Level
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
The Upper Half-Plane
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
Hecke Operators of Higher Level
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
Dirichlet Series and Modular Forms
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
The Petersson Inner Product
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
Some remarks related to Maeda's conjecture
|
2016
|
M. Ram Murty
Srinivas Kotyada
|
|
+
PDF
|
ON SIGN CHANGES FOR ALMOST PRIME COEFFICIENTS OF HALF‐INTEGRAL WEIGHT MODULAR FORMS
|
2016
|
Srilakshmi Krishnamoorthy
M. Ram Murty
|
|
+
|
The Modular Group
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
Problems in the Theory of Modular Forms
|
2016
|
M. Ram Murty
Michael Dewar
Hester Graves
|
|
+
|
A note on q-analogues of Dirichlet L-functions
|
2015
|
Alia Hamieh
M. Ram Murty
|
|
+
|
Transcendental values of the incomplete gamma function and related questions
|
2015
|
M. Ram Murty
Ekata Saha
|
|
+
|
Bertrand's Postulate for Number Fields
|
2015
|
Thomas A. Hulse
M. Ram Murty
|
|
+
PDF
Chat
|
On the error term in a Parseval type formula in the theory of Ramanujan expansions
|
2015
|
Giovanni Coppola
M. Ram Murty
Biswajyoti Saha
|
|
+
|
On sign changes for almost prime coefficients of half-integral weight modular forms
|
2015
|
Srilakshmi Krishnamoorthy
M. Ram Murty
|
|
+
PDF
|
On a conjecture of Erdős and certain Dirichlet series
|
2015
|
Tapas Chatterjee
M. Ram Murty
|
|
+
|
ON A CONJECTURE OF ERD ˝ OS AND CERTAIN DIRICHLET SERIES
|
2015
|
Tapas Chatterjee
M. Ram Murty
|
|
+
PDF
|
On the parity of the Fourier coefficients of $j$-function
|
2015
|
M. Ram Murty
R. Thangadurai
|
|
+
|
Some Remarks on Automorphy and the Sato-Tate Conjecture
|
2015
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Complex Analysis
|
2015
|
M. Ram Murty
|
|
+
|
Oscillations of coefficients of Dirichlet series attached to automorphic forms
|
2014
|
Jaban Meher
M. Ram Murty
|
|
+
|
On the nature of e and non-vanishing of derivatives of L-series at s= 1/2
|
2014
|
M. Ram Murty
Naomi Tanabe
|
|
+
|
Some remarks on iterated maps of natural numbers
|
2014
|
Agnes M. Herzberg
M. Ram Murty
|
|
+
|
An elliptic analogue of a theorem of Hecke
|
2014
|
M. Ram Murty
Akshaa Vatwani
|
|
+
|
Ramanujan — Fourier series and a theorem of Ingham
|
2014
|
H. Gopalakrishna Gadiyar
M. Ram Murty
R. Padma
|
|
+
|
Non-vanishing of Dirichlet series with periodic coefficients
|
2014
|
Tapas Chatterjee
M. Ram Murty
|
|
+
|
Non-vanishing of Dirichlet series with periodic coefficients
|
2014
|
Tapas Chatterjee
M. Ram Murty
|
|
+
|
A note on special values of 𝐿-functions
|
2014
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
PDF
|
Special values of the Gamma function at CM points
|
2014
|
M. Ram Murty
Chester Weatherby
|
|
+
|
Transcendence of Some Infinite Series
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
The Maximum Modulus Principle and Its Applications
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Liouville’s Theorem
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
The Modular Invariant
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendental Values of Some Elliptic Integrals
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendence of Values of Class Group L-Functions
|
2014
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Hermite’s Theorem
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendental Values of Eisenstein Series
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Siegel’s Lemma
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Estimates for Derivatives
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
The Lindemann–Weierstrass Theorem
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendental Values of Elliptic Functions
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Periods, Multiple Zeta Functions and ζ(3)
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Elliptic Integrals and Hypergeometric Series
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendental Values of Some Dirichlet Series
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Elliptic Functions
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendental Numbers
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
The Baker–Birch–Wirsing Theorem
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Linear Independence of Values of Dirichlet L-Functions
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
The Six Exponentials Theorem
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
More Elliptic Integrals
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Transcendence of Values of Modular Forms
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Some Applications of Baker’s Theorem
|
2014
|
M. Ram Murty
Purusottam Rath
|
|
+
|
Sign changes of Fourier coefficients of half-integral weight cusp forms
|
2013
|
Jaban Meher
M. Ram Murty
|
|
+
|
Littlewood and number theory
|
2013
|
M. Ram Murty
|
|
+
|
The twin prime problem and generalizations (après Yitang Zhang)
|
2013
|
M. Ram Murty
|
|
+
|
A family of number fields with unit rank at least 4 that has Euclidean ideals
|
2013
|
Hester Graves
M. Ram Murty
|
|
+
|
The abc conjecture and non-Wieferich primes in arithmetic progressions
|
2013
|
Hester Graves
M. Ram Murty
|
|
+
|
The Partition Function Revisited
|
2013
|
M. Ram Murty
|
|
+
|
Erratum to: The Ramanujan τ-Function
|
2013
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Ramanujan’s Proof of Bertrand’s Postulate
|
2013
|
Jaban Meher
M. Ram Murty
|
|
+
PDF
|
The work of K. Ramachandra in algebraic number theory
|
2013
|
M. Ram Murty
|
|
+
|
The Twin Prime Problem and Generalisations
|
2013
|
M. Ram Murty
GeneralisationsYitang Zhang
|
|
+
PDF
|
Ramanujan series for arithmetical functions
|
2013
|
M. Ram Murty
|
|
+
|
A derivation of the Hardy-Ramanujan formula from an arithmetic formula
|
2012
|
Michael Dewar
M. Ram Murty
|
|
+
|
A Bombieri-Vinogradov theorem for all number fields
|
2012
|
M. Ram Murty
Kathleen L. Petersen
|
|
+
|
Transcendence of Generalized Euler Constants
|
2012
|
M. Ram Murty
Anastasia Zaytseva
|
|
+
|
Some Nonlinear Identities for Divisor Functions
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Probabilistic Number Theory
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Ramanujan’s Conjecture and ℓ-Adic Representations
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Legacy of Srinivasa Ramanujan
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Prime Numbers and Highly Composite Numbers
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Ramanujan and Transcendence
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Ramanujan Conjecture from GL(2) to GL(n)
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Ramanujan τ-Function
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Arithmetic of the Partition Function
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Sato–Tate Conjecture for the Ramanujan τ-Function
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Circle Method
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Mock Theta Functions and Mock Modular Forms
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Mathematical Legacy of Srinivasa Ramanujan
|
2012
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
AN ASYMPTOTIC FORMULA FOR THE COEFFICIENTS OF j(z)
|
2012
|
Michael Dewar
M. Ram Murty
|
|
+
PDF
|
The Euclidean algorithm for number fields and primitive roots
|
2012
|
M. Ram Murty
Kathleen L. Petersen
|
|
+
PDF
|
A PROBLEM OF FOMENKO'S RELATED TO ARTIN'S CONJECTURE
|
2012
|
Adam Tyler Felix
M. Ram Murty
|
|
+
|
The uncertainty principle and a generalization of a theorem of Tao
|
2012
|
M. Ram Murty
Junho Peter Whang
|
|
+
PDF
Chat
|
ON A CONJECTURE OF ERDŐS
|
2012
|
Adam Tyler Felix
M. Ram Murty
|
|
+
PDF
|
Linear independence of Hurwitz zeta values and a theorem of Baker–Birch–Wirsing over number fields
|
2012
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
On a conjecture of Erdos
|
2012
|
Adam Tyler Felix
M. Ram Murty
|
|
+
|
A variant of the Lang–Trotter conjecture
|
2011
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
On a Conjecture of Chowla and Milnor
|
2011
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
A problem of Chowla revisited
|
2011
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Transcendental values of certain Eichler integrals
|
2011
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
ALGEBRAIC INDEPENDENCE OF VALUES OF MODULAR FORMS
|
2011
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
ON THE TRANSCENDENCE OF CERTAIN INFINITE SERIES
|
2011
|
M. Ram Murty
Chester Weatherby
|
|
+
|
AN ANALOGUE OF THE ERDÖS-KAK THEOREM FOR FOURIER COEFFICIENTS OF MODULAR FORMS
|
2011
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
L-Series and Transcendental Numbers
|
2011
|
M. Ram Murty
|
|
+
|
On a Problem of Ruderman
|
2011
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
The class number of $\mathbb{Q}(\sqrt{-p})$ and digits of $1/p$
|
2010
|
M. Ram Murty
R. Thangadurai
|
|
+
|
Transcendental values of class group L-functions
|
2010
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
Transcendental Nature of Special Values of <i>L</i>-Functions
|
2010
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
PDF
|
Euler–Lehmer constants and a conjecture of Erdös
|
2010
|
M. Ram Murty
N. Saradha
|
|
+
PDF
|
Small solutions of polynomial congruences
|
2010
|
M. Ram Murty
|
|
+
|
Corrigendum to “Transcendence of the log gamma function and some discrete periods” [J. Number Theory 129 (9) (2009) 2154–2165]
|
2009
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
PDF
|
Counting squarefree discriminants of trinomials under abc
|
2009
|
Anirban Mukhopadhyay
M. Ram Murty
Srinivas Kotyada
|
|
+
|
Transcendence of the log gamma function and some discrete periods
|
2009
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
Eulerian integral representations
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
The Kim-Sarnak theorem
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Generic representations and their Whittaker models
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Local 𝐿-functions: The non-Archimedean case
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Eisenstein series and constant terms
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Modular forms and their 𝐿-functions
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
𝐿-groups and automorphic 𝐿-functions
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Oscillations of Fourier coefficients of cusp forms
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Functoriality of the symmetric fourth
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Zeros and poles of Artin 𝐿-functions
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Introduction to Artin 𝐿-functions
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
PDF
Chat
|
Langlands functoriality conjecture
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
PDF
|
Meromorphic continuation of 𝐿-functions
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Kloosterman sums and Selberg’s conjecture
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Converse theorem of Cogdell and Piatetski-Shapiro
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
The Sato-Tate conjecture
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Fourier expansions and multiplicity one theorems
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Refined estimates for Fourier coefficients of cusp forms
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Local 𝐿-functions: The Archimedean case
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
Automorphic representations
|
2009
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
|
SPECIAL VALUES OF THE POLYGAMMA FUNCTIONS
|
2009
|
M. Ram Murty
N. Saradha
|
|
+
|
Hensel’s lemma
|
2009
|
M. Ram Murty
|
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+
|
Enumeration under Group Action
|
2009
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
|
Möbius Inversion and Graph Colouring
|
2009
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
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The Principle of Inclusion and Exclusion
|
2009
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
|
Matrices and Graphs
|
2009
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
|
Trees
|
2009
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
|
A First Course in Graph Theory and Combinatorics
|
2009
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
PDF
|
Summation methods and distribution of eigenvalues of Hecke operators
|
2008
|
Sanoli Gun
M. Ram Murty
Purusottam Rath
|
|
+
|
Problems in Analytic Number Theory
|
2008
|
M. Ram Murty
|
|
+
|
Expander graphs and gaps between primes
|
2008
|
Sebastian M. Cioabă
M. Ram Murty
|
|
+
|
Counting squarefree discriminants of trinomials under abc
|
2008
|
Anirban Mukhopadhyay
M. Ram Murty
Srinivas Kotyada
|
|
+
|
Pick's Theorem via Minkowski's Theorem
|
2007
|
M. Ram Murty
Nithum Thain
|
|
+
PDF
Chat
|
Representations of integers by certain positive definite binary quadratic forms
|
2007
|
M. Ram Murty
Robert Osburn
|
|
+
|
ODD VALUES OF FOURIER COEFFICIENTS OF CERTAIN MODULAR FORMS
|
2007
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Transcendental values of the digamma function
|
2007
|
M. Ram Murty
N. Saradha
|
|
+
|
Uniform Distribution of Zeros of Dirichlet Series
|
2007
|
Amir Akbary
M. Ram Murty
|
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+
|
An introduction to sieve methods and their applications
|
2006
|
Alina Cojocaru
M. Ram Murty
|
|
+
PDF
|
Multiple Hurwitz zeta functions
|
2006
|
M. Ram Murty
Kaneenika Sinha
|
|
+
PDF
|
The Bombieri–Vinogradov theorem
|
2005
|
Alina Carmen Cojocaru
M. Ram Murty
|
|
+
|
New directions in sieve theory
|
2005
|
Alina Carmen Cojocaru
M. Ram Murty
|
|
+
|
An Introduction to Sieve Methods and Their Applications
|
2005
|
Alina Carmen Cojocaru
M. Ram Murty
|
|
+
|
The lower bound sieve
|
2005
|
Alina Carmen Cojocaru
M. Ram Murty
|
|
+
|
A weighted Turán sieve method
|
2005
|
Yu-Ru Liu
M. Ram Murty
|
|
+
|
Ramanujan graphs and zeta functions
|
2005
|
M. Ram Murty
|
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+
|
Problems in Algebraic Number Theory
|
2005
|
M. Ram Murty
Jody Esmonde
|
|
+
PDF
|
On the 𝑝-adic series ∑_{𝑛=1}^{∞}𝑛^{𝑘}⋅𝑛!
|
2004
|
M. Ram Murty
Sarah Sumner
|
|
+
|
Lectures on Automorphic $L$-functions
|
2004
|
James Cogdell
Henry Kim
M. Ram Murty
|
|
+
PDF
|
Non-Abelian Generalizations of the Erdős-Kac Theorem
|
2004
|
M. Ram Murty
Filip Saidak
|
|
+
|
On the Uniform Distribution of Certain Sequences
|
2003
|
M. Ram Murty
Srinivas Kotyada
|
|
+
PDF
|
Irreducibility of Hecke polynomials
|
2003
|
Srinath Baba
M. Ram Murty
|
|
+
|
None
|
2003
|
M. Ram Murty
Srinivas Kotyada
|
|
+
PDF
|
On the number of real quadratic fields with class number divisible by 3
|
2002
|
Kalyan Chakraborty
M. Ram Murty
|
|
+
|
Prime Numbers and Irreducible Polynomials
|
2002
|
M. Ram Murty
|
|
+
|
Sieving Using Dirichlet Series
|
2002
|
M. Ram Murty
|
|
+
|
On Kummer's Conjecture
|
2001
|
M. Ram Murty
Yiannis N. Petridis
|
|
+
|
Primes in Arithmetic Progressions
|
2001
|
M. Ram Murty
|
|
+
|
p-adic Methods
|
2001
|
M. Ram Murty
|
|
+
|
The Method of Contour Integration
|
2001
|
M. Ram Murty
|
|
+
|
The Prime Number Theorem
|
2001
|
M. Ram Murty
|
|
+
PDF
|
Problems in Analytic Number Theory
|
2001
|
M. Ram Murty
|
|
+
|
Artin’s Conjecture for Primitive Roots
|
2001
|
M. Ram Murty
|
|
+
|
Arithmetic Functions
|
2001
|
M. Ram Murty
|
|
+
|
Arithmetic Functions
|
2001
|
M. Ram Murty
|
|
+
|
A simple derivation of $\zeta(1-K)=-B_K/K$
|
2000
|
M. Ram Murty
Marilyn Reece
|
|
+
|
Artin’s Conjecture for Polynomials Over Finite Fields
|
2000
|
Erik Jensen
M. Ram Murty
|
|
+
|
Artin’s Conjecture for Polynomials Over Finite Fields
|
2000
|
Erik Jensen
M. Ram Murty
|
|
+
|
On the order of 𝑎 (mod 𝑝)
|
1999
|
Pál Erdös
M. Ram Murty
|
|
+
|
None
|
1999
|
M. Ram Murty
Alberto Perelli
|
|
+
|
Bounds for congruence primes
|
1999
|
M. Ram Murty
|
|
+
|
Analytic Number Theory
|
1997
|
Yoichi Motohashi
Yoichi Motohashi
Enrico Bombieri
Enrico Bombieri
Enrico Bombieri
Jörg Brüdern
Jan‐Hendrik Evertse
John Friedlander
Andrew Granville
Adolf Hildebrand
|
|
+
|
Artin's Conjecture and Elliptic Analogues
|
1997
|
M. Ram Murty
|
|
+
|
Chapter 4 Modular Forms and Dirichlet Series
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Chapter 5 Dirichlet L-Functions
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
Non-vanishing of L-Functions and Applications
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Chapter 3 Equidistribution and L-Functions
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Chapter 7 Selberg’s Conjectures
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Chapter 8 Suggestions for Further Reading
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Non-Vanishing of Quadratic Twists of Modular L-Functions
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Equidistribution and L-Functions
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
The Prime Number Theorem and Generalizations
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Dirichlet L-Functions
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Selberg’s Conjectures
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Introduction
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Introduction
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Chapter 1 The Prime Number Theorem and Generalizations
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Chapter 6 Non-Vanishing of Quadratic Twists of Modular L-Functions
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Modular Forms and Dirichlet Series
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
|
Suggestions for Further Reading
|
1997
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
On the Distribution of Supersingular Primes
|
1996
|
Étienne Fouvry
M. Ram Murty
|
|
+
|
Selberg's Conjectures and Artin $L$-functions
|
1994
|
M. Ram Murty
|
|
+
|
A note on quadratic twists of an elliptic curve
|
1994
|
Liem Mai
M. Ram Murty
|
|
+
|
Elliptic Curves and Related Topics
|
1994
|
Hershy Kisilevsky
M. Ram Murty
|
|
+
PDF
|
On Zagier’s cusp form and the Ramanujan τ function
|
1994
|
Ashwaq Hashim
M. Ram Murty
|
|
+
PDF
|
Selberg’s conjectures and Artin 𝐿-functions
|
1994
|
M. Ram Murty
|
|
+
|
Mean Values of Derivatives of Modular L-Series
|
1991
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
Book Review: An introduction to the theory of the Riemann zeta-function
|
1989
|
M. Ram Murty
|
|
+
|
Modular Forms and the Chebotarev Density Theorem
|
1988
|
M. Ram Murty
V. Kumar Murty
N. Saradha
|
|
+
PDF
|
On The Number of Groups of Squarefree Order
|
1987
|
M. Ram Murty
Srimeenakshi Srinivasan
|
|
+
PDF
|
On the Sieve of Eratosthenes
|
1987
|
M. Ram Murty
S. Saradha
|
|
+
PDF
|
Some Remarks on Artin's Conjecture
|
1987
|
M. Ram Murty
Srimeenakshi Srinivasan
|
|
+
PDF
|
Odd values of the Ramanujan $\tau$-function
|
1987
|
M. Ram Murty
V. Kumar Murty
T. N. Shorey
|
|
+
PDF
|
On the estimation of eigenvalues of Hecke operators
|
1985
|
M. Ram Murty
|
|
+
|
An analogue of Artin's conjecture for Abelian extensions
|
1984
|
M. Ram Murty
|
|
+
|
On the number of groups of a given order
|
1984
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
On the density of various classes of groups
|
1983
|
M. Ram Murty
V. Kumar Murty
|
|
+
PDF
|
Oscillations of Fourier coefficients of modular forms
|
1983
|
M. Ram Murty
|
|
+
|
An ?-theorem for Ramanujan's ?-function
|
1982
|
R. Balasubramanian
M. Ram Murty
|
|
+
|
An ~2-Theorem for Ramanujan's z-Function
|
1982
|
R. Balasubramanian
M. Ram Murty
|
|
+
|
Some Ω-results for Ramanujan’s τ-function
|
1982
|
M. Ram Murty
|