SU\G(𝔸)/K·U
Mathematics › Algebra and Number Theory

Analytic Number Theory Research

Works Count: 35339

Description

This cluster of papers focuses on advanced research in prime number theory, L-functions, and their connections to topics such as the Riemann Zeta function, random matrix theory, arithmetic progressions, Vinogradov's mean value theorem, modular forms, and the distribution of primes. It also delves into the exploration of Euler's constant and its implications in number theory.

Keywords

Primes; L-Functions; Riemann Zeta Function; Random Matrix Theory; Arithmetic Progressions; Vinogradov's Mean Value Theorem; Modular Forms; Number Theory; Distribution of Primes; Euler's Constant

Most Cited Works

Action Title Date Authors
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On sets of integers containing k elements in arithmetic progression 1975-01-01 Endre Szemerédi
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Approximate formulas for some functions of prime numbers 1962-03-01 J. Barkley Rosser Lowell Schoenfeld
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The Arithmetic of Elliptic Curves 1986-01-01 Joseph H. Silverman
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Series Associated with the Zeta and Related Functions 2001-01-01 H. M. Srivastava Junesang Choi
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Topics in Classical Automorphic Forms 1997-10-10 Henryk Iwaniec
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Random Matrices, Frobenius Eigenvalues, and Monodromy 1998-11-24 Nicholas M. Katz Peter Sarnak
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Theta Functions on Riemann Surfaces 1973-01-01 John D. Fay
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Introduction to Cyclotomic Fields 1982-01-01 Lawrence C. Washington
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Modular Functions and Dirichlet Series in Number Theory 1990-01-01 Tom M. Apostol
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Advanced Topics in the Arithmetic of Elliptic Curves 1994-01-01 Joseph H. Silverman
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On the Functional Equations Satisfied by Eisenstein Series 1976-01-01 R. P. Langlands
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Transcendental Number Theory 1975-04-24 A. Baker
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L-Functions and Tamagawa Numbers of Motives 2007-01-01 Spencer Bloch Kazuya Katô
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On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises 2001-05-15 Christophe Breuil Brian Conrad Fred Diamond Richard Taylor
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Values of Zeta Functions and Their Applications 1994-01-01 Don Zagier
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Hecke operators on ?0(m) 1970-06-01 A. O. L. Atkin Joseph Lehner
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Factoring Integers with Elliptic Curves 1987-11-01 H. W. Lenstra
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Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis 1994-10-11 Hugh L. Montgomery
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Topics in Analytic Number Theory 1973-01-01 Hans Rademacher
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Longest Increasing and Decreasing Subsequences 2009-01-01 C. Schensted
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Representation of Lie Groups and Special Functions 1992-01-01 N. Ja. Vilenkin A. U. Klimyk
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Abelian l-Adic Representations and Elliptic Curves 1997-11-15 Jean-Pierre Serre
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Asymptotic Formulaae in Combinatory Analysis 1918-01-01 G. H. Hardy S. Ramanujan
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Zeros of principal L-functions and random matrix theory 1996-01-01 Zeév Rudnick Peter Sarnak
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Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes 1923-01-01 G. H. Hardy J. E. Littlewood
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INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS 1980-02-28 Vadim V. Nikulin
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An approximation of partial sums of independent RV's, and the sample DF. II 1976-01-01 J. Koml�s Péter Major G. Tusn�dy
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Ein Satz �ber Untermengen einer endlichen Menge 1928-12-01 Emanuel Sperner
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A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs 1980-12-01 Béla Bollobás
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The primes contain arbitrarily long arithmetic progressions 2008-03-01 Benjamin Green Terence Tao
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On the normal concentration of divisors, 2 2009-07-06 Helmut Maier Gérald Tenenbaum
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On Certain Sets of Integers 1953-01-01 K. F. Roth
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Factoring polynomials with rational coefficients 1982-12-01 A. K. Lenstra H. W. Lenstra László Lovász
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PRIMES is in P 2004-09-01 Manindra Agrawal Neeraj Kayal Nitin Saxena
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The development of the number field sieve 1993-01-01
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Spectral Methods of Automorphic Forms 2002-11-19 Henryk Iwaniec
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Introduction to the Arithmetic Theory of Automorphic Functions 1972-10-01 Marvin Tretkoff Goro Shimura
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Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire 1943-07-01 B Gnedenko
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Modular Elliptic Curves and Fermat's Last Theorem 1995-05-01 Andrew Wiles
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A new proof of Szemerédi's theorem 2001-08-15 W. T. Gowers
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Quadratic and Hermitian Forms 1985-01-01 Winfried Scharlau
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The lost notebook and other unpublished papers 1989-07-01 Srinivasa Ramanujan Aiyangar George E. Andrews
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Algebraic number theory 1999-11-22 Kazuya Katô Nobushige Kurokawa Takeshi Saito
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Singular Integrals and Differentiability Properties of Functions (PMS-30) 1971-12-31 Elias M. Stein
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On Modular Forms of Half Integral Weight 1973-05-01 Goro Shimura
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The Arithmetic of Dynamical Systems 2007-01-01 Joseph H. Silverman
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An approximation of partial sums of independent RV'-s, and the sample DF. I 1975-01-01 J. Koml�s Péter Major G. Tusn�dy
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The Arithmetic of Elliptic Curves 2009-01-01 Joseph H. Silverman
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An Introduction To The Theory Of Numbers 2008-07-31 G. H. Hardy E. M. Wright
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Zeta and q-Zeta Functions and Associated Series and Integrals 2012-01-01 H. M. Srivastava June-Sang Choi

Most Recent Works

Action Title Date Authors
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Unimodal sequences and mixed false theta functions 2025-04-25 Kevin Allen Robert Osburn
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On the $$L_2$$-discrepancy of Latin hypercubes 2025-04-25 Nicolas Nagel
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The Asymptotics of Coefficients of Dedekind Zeta Functions on Certain Integral Binary Quadratic Forms 2025-04-26 Guodong Hua
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New Concepts of Congruences Modulo 1/n and Positive Integers Modulo 1/n 2025-04-25 Habib Lebsir
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More <i>q</i> -analogs of congruences involving Catalan numbers 2025-04-25 Roberto Tauraso
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Strange and pseudo-differentiable functions with applications to prime partitions 2025-04-26 A. Dong Nicolas Robles Alexandru Zaharescu Dirk Zeindler
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$$L^{\infty }$$-norm bounds for Jacobi cusp forms 2025-04-26 Anilatmaja Aryasomayajula Jürg Kramer Anna-Maria von Pippich
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Mordell-Tornheim zeta functions and functional equations for Herglotz-Zagier type functions 2025-04-28 Atul Dixit Sumukha Sathyanarayana N. Guru Sharan
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On an optimal problem of bilinear forms 2025-04-28 Naihuan Jing Yibo Liu Jiacheng Sun Chengrui Zhao Haoran Zhu
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On the Kohayakawa–Kreuter conjecture 2025-04-28 Eden Kuperwasser Wojciech Samotij Yuval Wigderson
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Trig Functions and Complex Numbers 2025-04-27
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On the Action of a Subgroup of the Modular Group on Imaginary Quadratic Number Fields 2025-04-27 Abdulaziz Deajim
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On Sylvester’s denumerants 2025-04-29 Eteri Samsonadze
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A general formula for Hecke-type false theta functions 2025-04-29 Eric T. Mortenson
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Quantum-Consistent Adelic Integration and Structure of Egyptian Fractions 2025-04-29 J. Bel
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Complete 3-term arithmetic progression free sets of small size in vector spaces and other abelian groups 2025-04-30 Bence Csajbók Zoltán Lóránt Nagy
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An In-Depth Investigation of the Riemann Zeta Function Using Infinite Numbers 2025-04-30 Emmanuel Thalassinakis
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On several irrationality problems for Ahmes series 2025-05-01 Vjekoslav Kovač Terence Tao
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Bounds on Erdos - Faber - Lovász conjecture - the uniform and regular cases 2025-04-28 S. M. Hegde Suresh Dara
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On alternative definition of Lucas atoms and their p-adic valuations 2025-05-02 Gessica Alecci Piotr Miska Nadir Murru Giuliano Romeo
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A note on the density of zeros of partial sums of the Dirichlet lambda, beta and eta functions 2025-05-02 Eric Dubon
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CHAPTER 10 One-parameter families of exponential sums 2025-05-04
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CHAPTER 11 Multi-parameter families of exponential sums 2025-05-04
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Splitting of almost ordinary abelian surfaces in families and the 𝑆-integrality conjectures 2025-05-05 Ruofan Jiang
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Ratios of consecutive values of the divisor function 2025-04-27 Sean Eberhard
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Cyclotomic primes 2025-05-01 Carl Pomerance
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Consecutive Piatetski-Shapiro primes based on the Hardy-Littlewood conjecture 2025-05-01 Victor Zhenyu Guo Yuan Yi
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Joint cubic moment of Eisenstein series and Hecke-Maass cusp forms 2025-05-01 Charng Rang Guo
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Rational deformations of the set of multiple zeta-star values 2025-05-01 Jiangtao Li
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The irrationality of an infinite series involving ω(n) under a prime tuples conjecture 2025-05-01 Kyle Pratt
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Class Numbers, Congruent Numbers and Umbral Moonshine 2025-05-01 Miranda C. N. Cheng John F. R. Duncan Michael H. Mertens
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Generation of cyclotomic Hecke fields by L-values of cusp forms on GL(2) with certain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math> twist 2025-05-01 Jaesung Kwon
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Divisibility of the multiplicative order modulo monic irreducible polynomials over finite fields 2025-05-01 J. Conceição
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Multiplicative generalised polynomial sequences 2025-05-01 Jakub Konieczny
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Maesaka–Seki–Watanabe's formula for multiple harmonic q-sums 2025-05-01 Yuto Tsuruta
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Hook length biases for self-conjugate partitions and partitions with distinct odd parts 2025-05-01 Catherine Cossaboom
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New congruences modulo powers of 2 for certain t-regular partitions 2025-05-06 Wu Jie Doris D. M. Sang Olivia X. M. Yao
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On K-moduli of quartic threefolds 2025-05-01 Hamid Abban Ivan Cheltsov Alexander Kasprzyk Yuchen Liu Andrea Petracci
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A New q-Supercongruence Modulo the Fourth Power of a Cyclotomic Polynomial 2025-05-06 Dandan Chen Qingquan Deng
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Unit group of some triquadratic number fields and Greenberg’s conjecture 2025-05-06 Abdellah Sbai Idriss Jerrari Abdelmalek Azizi
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Period function of Maass forms from Ramanujan's lost notebook 2025-05-06 YoungJu Choie Rahul Kumar
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Five-point functions and the permutation group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>S</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:math> 2025-05-07 Gernot Eichmann R. Torres
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Measures associated with certain ellipsephic series and the allouche-hu-morin limit theorem 2025-05-07 Jean-François Burnol
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Chebyshev polynomials boost the π-series convergence 2025-05-07 Sungwoong Cho Daekyoung Kang U-Rae Kim Jungil Lee Jiawei Zhu
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Approximation of analytic functions by generalized discrete shifts of the Lerch zeta-function 2025-05-08 Antanas Laurinčikas Toma Mikalauskaitė Darius Šiaučiūnas
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Sum of the Epstein zeta function over the Riemann zeta function zeros 2025-05-08 Ramūnas Garunkštis Tomas Kondratavičius Jokūbas Putrius
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On the number of zeros of L−functions attached to cusp forms of half-integral weight 2025-05-01 Pedro Ribeiro
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Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms 2025-05-01 Palak Arora Glenn Bruda Bruce Fang Raúl A. Márquez Steven J. Miller Beni Prapashtica Vismay Sharan Donghoon Son Xueyiming Tang Saad Waheed
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Pair correlations, beta distribution and hypergeometric functions 2025-05-09 Christian Weiß
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Proof of Some Conjectural Congruences Involving Binomial Coefficients and Apéry-like Numbers 2025-05-05 Guo-Shuai Mao