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

Abstract

We obtain some new properties of the signal generated by the Riemann zeta-function in this paper. Namely, we show the connection between the function $\zf$ and a nonlinear integral equation related to the Poisson-Lobachevsky integral.

References in corpus (4)

• 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 new orthogonal systems generated by Jacobi polynomials
• Jacob's ladders, Bessel's functions and the asymptotic solutions of a new class of nonlinear integral equations