Jacob's ladders, Bessel's functions and the asymptotic solutions of a new class of nonlinear integral equations

TL;DR

This paper explores the relationship between the Riemann zeta-function and Bessel functions, introducing a new class of nonlinear integral equations and analyzing their asymptotic solutions.

Contribution

It establishes a novel connection between the Riemann zeta-function and Bessel functions, and introduces a new class of nonlinear integral equations.

Findings

Connection between Riemann zeta-function and Bessel functions established

Introduction of a new class of nonlinear integral equations

Asymptotic solutions analyzed for the new equations

Abstract

It is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the Bessel's functions. In this direction, a new class of the nonlinear integral equations is introduced.