Corpus ID: 182557443

# Modular-type transformations and integrals involving the Riemann ?-function

@inproceedings{Dixit2018ModulartypeTA,
title={Modular-type transformations and integrals involving the Riemann ?-function},
author={A. Dixit},
year={2018}
}
A survey of various developments in the area of modular-type transformations (along with their generalizations of different types) and integrals involving the Riemann Ξ-function associated to them is given. We discuss their applications in Analytic Number Theory, Special Functions and Asymptotic Analysis.
3 Citations
On Hurwitz zeta function and Lommel functions
• Mathematics
• 2019
We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function $\zeta(s, a)$ beginning with Hermite's formula. The aim is to reveal a nice connection between $\zeta(s, a)$ and a specialExpand
Ramanujan's Beautiful Integrals
• Mathematics
• 2021
Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the Journal of the Indian Mathematical Society, notebooks,Expand
Superimposing theta structure on a generalized modular relation
• Mathematics
• 2020
A generalized modular relation of the form $F(z, w, \alpha)=F(z, iw,\beta)$, where $\alpha\beta=1$ and $i=\sqrt{-1}$, is obtained in the course of evaluating an integral involving the RiemannExpand

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