The Riemann Hypothesis in Oaxaca

TL;DR

This paper establishes a combinatorial equivalence of the Riemann Hypothesis using the Young lattice and integer partitions, linking classical number theory thresholds to combinatorial structures.

Contribution

It introduces a novel combinatorial framework connecting the Riemann Hypothesis to the Young lattice and integer partitions, providing a new perspective on classical number theory thresholds.

Findings

Classical threshold related to sum-of-divisors function is realized combinatorially.

A direct bridge between the Riemann Hypothesis and the Young lattice is established.

Limiting proportions of integer partitions reflect the asymptotic behavior of number-theoretic functions.

Abstract

An equivalence of the Riemann Hypothesis (RH) enables a direct bridge to the Young lattice. In specific, the classical threshold $\lim_{n\to\infty} \sigma(n)/(n \log\log n) = e^{\gamma} \approx 1.78107$, derived from the asymptotic behavior of the sum-of-divisors function, can be realized combinatorially via limiting proportions associated to specific families of integer partitions.