English

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}
}