New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan

Bruce C. Berndt, Atul Dixit, Arindam Roy, Alexandru Zaharescu

Type: Article

Publication Date: 2016-09-21

Citations: 26

DOI: https://doi.org/10.1016/j.aim.2016.08.011

View Publication

Locations

Advances in Mathematics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	New pathways and connections in Number Theory and Analysis motivated by two incorrect claims of Ramanujan	2016	Bruce C. Berndt Atul Dixit Arindam Roy Alexandru Zaharescu
+	New pathways and connections in Number Theory and Analysis motivated by two incorrect claims of Ramanujan	2016	Bruce C. Berndt Atul Dixit Arindam Roy Alexandru Zaharescu
+	Ramanujan's Thoughts from God	2017	Frank Aiello
+	Ramanujan's Thoughts from God	2017	Frank Aiello
+ PDF Chat	Questionable claims found in Ramanujan’s lost notebook	2008	Bruce C. Berndt O-Yeat Chan Sung-Geun Lim Alexandru Zaharescu
+ PDF Chat	On a Pair of Identities from Ramanujan's Lost Notebook	2012	James McLaughlin Andrew V. Sills
+ PDF Chat	Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities	2022	Subhash Chand Bhoria Pramod Eyyunni Bibekananda Maji
+	Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities	2020	Subhash Chand Bhoria Pramod Eyyunni Bibekananda Maji
+	Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities	2020	Subhash Chand Bhoria Pramod Eyyunni Bibekananda Maji
+	An Overview of Ramanujan's Notebooks	1998	Bruce C. Berndt
+	Analytic and Combinatorial Number Theory: The Legacy of Ramanujan	2023	George E. Andrews Michael Filaseta Ae Ja Yee
+	An Introduction to Ramanujan's "lost" Notebook	1979	George E. Andrews
+	An introduction to Ramanujan’s “lost” notebook	2001	George E. Andrews
+	Ramanujan’s Lost Notebook	2005	George E. Andrews Bruce C. Berndt
+	Generalizations (in the spirit of Koshliakov) of some formulas from Ramanujan's Lost Notebook	2023	Pedro Ribeiro Semyon Yakubovich
+	Ramanujan's Formula for $\zeta(2n+1)$	2017	Bruce C. Berndt Armin Straub
+ PDF Chat	Uncovering Ramanujan’s “Lost” Notebook: an oral history	2012	Robert Schneider
+	Combinatorics and Ramanujan's “Lost” Notebook	1985	George E. Andrews
+ PDF Chat	A WZ PROOF OF RAMANUJAN’S FORMULA FOR π	1995	Shalosh B. Ekhad Doron Zeilberger
+	Ramanujan's Formula for $ζ(2n+1)$	2017	Bruce C. Berndt Armin Straub

Works That Cite This (26)

Action	Title	Year	Authors
+	Partitions with multiplicities associated with divisor functions	2023	Bruce C. Berndt Nicolas Robles Alexandru Zaharescu Dirk Zeindler
+ PDF Chat	Character analogues of Cohen-type identities and related Voronoï summation formulas	2023	Debika Banerjee Khyati Khurana
+	On squares of odd zeta values and analogues of Eisenstein series	2019	Atul Dixit Rajat Gupta
+	Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts	2018	Atul Dixit Rahul Kumar Bibekananda Maji Alexandru Zaharescu
+ PDF Chat	Extended higher Herglotz functions I. Functional equations	2023	Atul Dixit Rajat Gupta Rahul Kumar
+	Explicit transformations for generalized Lambert series associated with the divisor function $$\sigma _{a}^{(N)}(n)$$ and their applications	2023	Soumyarup Banerjee Atul Dixit Shivajee Gupta
+	Commentary on and Corrections to the First Four Volumes	2018	George E. Andrews Bruce C. Berndt
+ PDF Chat	Generalized Lambert series and arithmetic nature of odd zeta values	2019	Atul Dixit Bibekananda Maji
+	Applications of the Lipschitz Summation Formula and a Generalization of Raabe’s Cosine Transform	2023	Atul Dixit Rahul Kumar
+	GENERALIZED LAMBERT SERIES, RAABE’S COSINE TRANSFORM AND A GENERALIZATION OF RAMANUJAN’S FORMULA FOR	2018	Atul Dixit Rajat Gupta Rahul Kumar Bibekananda Maji

Works Cited by This (76)

Action	Title	Year	Authors
+	The Voronoï summation formula	1972	Bruce C. Berndt
+ PDF Chat	The mean square of the error term in a generalization of Dirichlet's divisor problem	1996	Tom Meurman
+	The Voronoi Identity via the Laplace Transform	1998	Aleksandar Ivić
+ PDF Chat	Tables of Integral Transforms	2005	Bateman Manuscript H. Bateman Arthur Erdélyi
+ PDF Chat	Introduction to Analytic Number Theory	1976	Tom M. Apostol
+	Multiplicative Number Theory	1980	H. Davenport
+	<i>Theory of Functions of a Complex Variable</i>	1966	A. I. Markushevich Richard A. Silverman J. Gillis
+	Lectures on a Method in the Theory of Exponential Sums	1987	Matti Jutila
+	None	2003	K. Soundararajan
+	Hecke's Functional Equation and Arithmetical Identities	1961	K. Chandrasekharan Raghavan Narasimhan