Year: 2019
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: D'Isanto, Paolo, Esposito, Giampiero
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2912428857