Sandwiching the Riemann hypothesis

TL;DR

This paper explores a sandwiching method involving three analytic functions, two with zeros on the critical line, to derive constraints on the third function's zeros and convergence properties, offering new insights into the Riemann hypothesis.

Contribution

It introduces a novel inequality-based approach to analyze the zeros of the Riemann zeta function through a sandwiching technique involving three analytic functions.

Findings

Constraints on the third function's zeros derived from inequalities

Insights into the radius of convergence of expansions of s(s)

Potential implications for the Riemann hypothesis

Abstract

We consider a system of three analytic functions, two of which are known to have all their zeros on the critical line $\Re (s)=\sigma=1/2$. We construct inequalities which constrain the third function, $\xi(s)$, on $\Im(s)=0$ to lie between the other two functions, in a sandwich structure. We investigate what can be said about the location of zeros and radius of convergence of expansions of $\xi(s)$, with promising results.