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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…
Normality from one family of meromorphic functions to another through sharing of values
Kuldeep Singh Charak, Manish Kumar, Rahul Kumar
Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such th…
Some variations on an extension of Caratheodory's normality criterion
Kuldeep Singh Charak, Rahul Kumar
In this note we give some variations on an extension of Caratheodory's normality criterion due to Grahl and Nevo.
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…