TITLE:
On the Absence of Zeros of Riemann Zeta-Function Out of ℜ(z) = 1/2
AUTHORS:
Jorge Julián Sánchez Martínez
KEYWORDS:
Riemann Zeta Function, Analyticity, Weierstrass-Hadamard Product, Representation
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.3,
March
18,
2022
ABSTRACT: This work shows, after a brief introduction to Riemann zeta function , the demonstration that all non-trivial zeros of this function lies on the so-called “critical line”,, the one Hardy demonstrated in his famous work that infinite countable zeros of the above function can be found on it. Thus, out of this strip, the only remaining zeros of this function are the so-called “trivial ones” . After an analytical introduction reminding the existence of a germ from a generic zero lying in , we show through a Weierstrass-Hadamard representation approach of the above germ that non-trivial zeros out of cannot be found.