1 citations · 4 across the 10 of their papers we have counts for
13 papers
A note on odd zeta values over any number field and Extended Eisenstein series
Soumyarup Banerjee, Rajat Gupta, Rahul Kumar
In this article, we have studied transformation formulas of zeta function at odd integers over an arbitrary number field which in turn generalizes Ramanujan's identity for the Riem…
Modified Bessel Functions in Analytic Number Theory
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
The modified Bessel functions , or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic ident…
Two General Series Identities Involving Modified Bessel Functions and a Class of Arithmetical Functions
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
We consider two sequences and , , generated by Dirichlet series $$\sum_{n=1}^{\infty}\frac{a(n)}{λ_n^{s}}\qquad\text{and}\qquad \sum_{n=1}^{\infty}\fra…
Extended Higher Herglotz function \textup{II}
Rajat Gupta, Rahul Kumar
Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Noteb…
Ramanujan and Koshliakov Meet Abel and Plana
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
The neglected Russian mathematician, N.~S.~Koshliakov, derived beautiful generalizations of the classical Abel--Plana summation formula through a setting arising from a boundary va…
A Class of Identities Associated with Dirichlet Series Satisfying Hecke's Functional Equation
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
We consider two sequences and , , generated by Dirichlet series of the forms $$\sum_{n=1}^{\infty}\frac{a(n)}{λ_n^{s}}\qquad\text{and}\qquad \sum_{n=1}…
Koshliakov zeta functions I: Modular Relations
Atul Dixit, Rajat Gupta
We examine an unstudied manuscript of N.~S.~Koshliakov over pages long and containing the theory of two interesting generalizations and of the Riemann zeta…
Extended higher Herglotz functions I. Functional equations
Atul Dixit, Rajat Gupta, Rahul Kumar
In 1975, Don Zagier obtained a new version of the Kronecker limit formula for a real quadratic field which involved an interesting function which is now known as the \emph{H…
On a certain divisor function in Number fields
Rajat Gupta, Sudip Pandit
The main aim of this paper is to study an analogue of the generalized divisor function in a number field , namely, . The Dirichlet series associate…
Generalizations of the Andrews-Yee identities associated with the mock theta functions and
Bruce C. Berndt, Atul Dixit, Rajat Gupta
George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third order mock theta functions and , thereby extending…
On Sum-Of-Tails Identities
Rajat Gupta
In this article, a finite analogue of the generalized sum-of-tails identity of Andrews and Freitas is obtained. We derive several interesting results as special cases of this analo…
A Ramanujan-type formula for and its generalizations
Atul Dixit, Rajat Gupta
A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein ser…
Generalized Lambert series, Raabe's integral and a two-parameter generalization of Ramanujan's formula for
Atul Dixit, Rajat Gupta, Rahul Kumar +1
A comprehensive study of the generalized Lambert series , and…