Schoenberg's Theory of Totally Positive Functions and the Riemann Zeta Function

TL;DR

This paper reviews Schoenberg's theory of totally positive functions, explores its connection to the Laguerre-Polya class, and presents a new condition equivalent to the Riemann hypothesis.

Contribution

It introduces a novel condition linking Schoenberg's theory to the Riemann hypothesis, expanding the theoretical framework of totally positive functions.

Findings

New condition equivalent to the Riemann hypothesis

Connection established between Schoenberg's theory and Laguerre-Polya class

Enhanced understanding of totally positive functions

Abstract

We review Schoenberg's characterization of totally positive functions and its connection to the Laguerre-Polya class. This characterization yields a new condition that is equivalent to the truth of the Riemann hypothesis.