An analytic approach to the Riemann hypothesis
Complex Variables
2021-07-22 v3
Abstract
In this work we consider an equation for the Riemann zeta-function in the critical half-strip. With the help of this equation we prove that finding non-trivial zeros of the Riemann zeta-function outside the critical line would be equivalent to the existence of complex numbers for which equation (5.1) in the paper holds. Such a condition is studied, and the attempt of proving the Riemann hypothesis is found to involve also the functional equation (6.26), where t is a real variable bigger than or equal to 1 and n is any natural number. The limiting behavior of the solutions as t approaches 1 is then studied in detail.
Cite
@article{arxiv.1902.04746,
title = {An analytic approach to the Riemann hypothesis},
author = {Paolo D'Isanto and Giampiero Esposito},
journal= {arXiv preprint arXiv:1902.04746},
year = {2021}
}
Comments
30 pages, 2 figures. In the final version, the presentation has been improved