On zeros of the Riemann zeta function

TL;DR

This paper demonstrates that the zeros of the Riemann zeta function in the critical strip coincide with those of a specific integral function and explores the properties of this integral function.

Contribution

It establishes a new equivalence between the zeros of the Riemann zeta function and an integral function, providing insights into their behavior.

Findings

Zeros of ζ(s) and F(s) coincide in the critical strip

Analysis of the behavior of the integral function F(s)

Potential implications for understanding the distribution of zeros

Abstract

This paper shows that, in the critical strip, the Riemann zeta function $\zeta(s)$ have the same set of zeros as $F(s):=\int_0^\infty t^{s-1}(e^t+1)^{-1}dt$, and then discusses the behavior of $F(s)$.