arXiv subjects

M. P. Chaudhary

Publications and source records attributed to M. P. Chaudhary.

2 recordsLinked to original sources

arXiv2025

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions

Generalized $m$-gonal numbers are those $p_m(x)= [ (m - 2)x^2 - (m - 4)x ]/2 $ where $x$ and $m$ are integers with $m \geq 3$. If any nonnegative integer can be written in the form $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$, where $a,b,c,d$ are positive integers, then we call $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$ a universal quaternary sum. In this paper, we determine the universality of many quaternary sums when $r,s,t,u \in \{3,4,5,8\}$, using the theory of Ramanujan's theta function identities

math.NT↗

arXiv2016

Integrals of products of Hurwitz zeta functions and the Casimir effect in $ϕ^4$ field theories

We evaluate two integrals over $x\in [0,1]$ involving products of the function $ζ_1(a,x)\equiv ζ(a,x)-x^{-a}$ for $\Re (a)>1$, where $ζ(a,x)$ is the Hurwitz zeta function. The evaluation of these integrals for the particular case of integer $a\geq 2$ is also presented. As an application we calculate the $O(g)$ weak-coupling expansion coefficient $c_{1}(\varepsilon)$ of the Casimir energy for a film with Dirichlet-Dirichlet boundary conditions, first stated by Symanzik [Schrödinger representation and Casimir effect in renormalizable quantum field theory, Nucl. Phys. B 190 (1981) 1-44] in the framework of $gϕ^4_{4-\varepsilon}$ theory.

math.CA↗