1 citations · 3 across the 8 of their papers we have counts for
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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 $$\sum_{n=1}^{\infty}\frac{a(n)}{λ_n^{s}}\qquad\text{and}\qquad \sum_{n=1}^{\infty}\fra…
Extended Higher Herglotz function \textup{II}
Rajat Gupta, Rahul Kumar
Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Noteb…
A Class of Identities Associated with Dirichlet Series Satisfying Hecke's Functional Equation
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
We consider two sequences and , , generated by Dirichlet series of the forms $$\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…