On Salem's Integral Equation and related criteria
Number Theory
2024-03-20 v2
Abstract
We extend Salem's Integral equation to the non-homogenous form, and offer the associated criteria for the Riemann Hypothesis. Explicit solutions for the non-homogenous case are given, which in turn give further insight into Salem's criteria for the RH. As a conclusion, we show these results follow from a corollary relating the uniqueness of solutions of the non-homogenous form with Wiener's theorem.
Keywords
Cite
@article{arxiv.2003.00581,
title = {On Salem's Integral Equation and related criteria},
author = {Alexander E Patkowski},
journal= {arXiv preprint arXiv:2003.00581},
year = {2024}
}