Yet Another Riemann Hypothesis

TL;DR

This paper explores a novel generalization of the Riemann hypothesis involving permutation groups acting on continued fractions, supported by numerical evidence suggesting a broad class of functions may satisfy the hypothesis.

Contribution

It introduces a new generalization of the Riemann hypothesis based on permutation group actions on continued fractions and provides numerical survey results.

Findings

Numerical results suggest many functions obey the Riemann hypothesis.

Shared non-trivial zeros among these functions are observed.

Broad class of functions may satisfy the hypothesis.

Abstract

This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and thus this note focuses on providing a numerical survey. These results indicate a broad class of previously unexamined functions may obey the Riemann hypothesis in general, and even share the non-trivial zeros in particular.