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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…
Number field analogue of divisor function à la Koshliakov
Soumyarup Banerjee, Rahul Kumar
In this article, we study a divisor function in an arbitrary number field akin to Koshliakov's work on Vorono\"{\dotlessi} summation formula. More precisely, we generalize Koshliak…
Explicit identities on zeta values over imaginary quadratic field
Soumyarup Banerjee, Rahul Kumar
In this article, we study special values of the Dedekind zeta function over an imaginary quadratic field. The values of the Dedekind zeta function at any even integer over any tota…
Extensions of Watson's theorem and the Ramanujan-Guinand formula
Rahul Kumar
Ramanujan provided several results involving the modified Bessel function in his Lost Notebook. One of them is the famous Ramanujan-Guinand formula, equivalent to the func…
Superimposing theta structure on a generalized modular relation
Atul Dixit, Rahul Kumar
A generalized modular relation of the form , where and , is obtained in the course of evaluating an integral involving the Riemann -fu…
On Hurwitz zeta function and Lommel functions
Atul Dixit, Rahul Kumar
We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function beginning with Hermite's formula. The aim is to reveal a nice connection between and a…