23 citations · 35 across the 50 of their papers we have counts for
5 papers · 2 filters
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…
Ramanujan's Beautiful Integrals
Bruce C. Berndt, Atul Dixit
Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the \emph{Journal of the Indian Mathematical…