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

References in corpus (7)

• Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral
• Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral
• Jacob's ladders and the quantization of the Hardy-Littlewood integral
• Jacob's ladders and the first asymptotic formula for the expression of the fifth order $Z^3[...]{\hat{Z}}^2(t)$ for the collection of disconnected sets
• Jacob's ladders and the almost exact asymptotic representation of the Hardy-Littlewood integral
• Jacob's ladders and the asymptotically approximate solutions of a nonlinear diophantine equation
• Jacob's ladders and new orthogonal systems generated by Jacobi polynomials

Cited by in corpus (1)

• Jacob's ladders and some nonlinear integral equations connected with the Poisson-Lobachevsky integral