Atul Dixit

activity

20092026

most citedGeneralized Lambert series and arithmetic nature of odd zeta values

23 citations · 35 across the 50 of their papers we have counts for

collaborators

Showing 2019Show all

4 papers · 1 filter

math.NT2019

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 $ζ (s, a)$ beginning with Hermite's formula. The aim is to reveal a nice connection between $ζ (s, a)$ and a…

math.NT2019

Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory

Atul Dixit, Arindam Roy

Closed-form evaluations of certain integrals of $J_{0} (ξ)$ , the Bessel function of the first kind, have been crucial in the studies on the electromagnetic field of alternating curr…

math.CO2019

A simple proof of a congruence for a series involving the little $q$ -Jacobi polynomials

Atul Dixit

We give a simple and a more explicit proof of a mod $4$ congruence for a series involving the little $q$ -Jacobi polynomials which arose in a recent study of a certain restricted ov…

math.NT2019

A Ramanujan-type formula for $ζ^{2} (2 m + 1)$ and its generalizations

Atul Dixit, Rajat Gupta

A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein ser…

On Hurwitz zeta function and Lommel functions

Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory

A simple proof of a congruence for a series involving the little q-Jacobi polynomials

A Ramanujan-type formula for ζ2(2m+1) and its generalizations

A simple proof of a congruence for a series involving the little $q$ -Jacobi polynomials

A Ramanujan-type formula for $ζ^{2} (2 m + 1)$ and its generalizations