Modulus representation of the Riemann $\xi$ function and polynomial inequalities equivalent to the Riemann hypothesis
Number Theory
2024-11-07 v3
Abstract
We use the Jacobi theta function to give a representation of the modulus of the Riemann function. Based on this modulus representation, we show that the Riemann hypothesis is equivalent to the validity of a family of polynomial inequalities. We also present some preliminary results on the polynomial inequalities.
Keywords
Cite
@article{arxiv.2404.06642,
title = {Modulus representation of the Riemann $\xi$ function and polynomial inequalities equivalent to the Riemann hypothesis},
author = {Wei Sun},
journal= {arXiv preprint arXiv:2404.06642},
year = {2024}
}