A Conjecture Regarding the Riemann Hypothesis as Visualized by t strings

TL;DR

This paper introduces a heuristic string visualization approach to study the Riemann Hypothesis, revealing an organizing principle and a generic structure that offer new insights into the distribution of zeros of the Zeta function.

Contribution

It proposes a novel string-based visualization method and extends the domain analysis to provide a new perspective on the Riemann Hypothesis.

Findings

Visual evidence supporting the hypothesis

Identification of an organizing principle for strings

Expanded domain analysis reveals structural insights

Abstract

The introduction of strings into the study of the Riemann Hypothesis provides a visualization of the genesis of zeros for the Zeta function. The method is heuristic and when originally introduced suggested strong visual evidence for the truth of the Riemann Hypothesis. Some sort of organizing principle for strings with similar t values is observed and points towards a region between (1, 0) and (0, 0) on the abscissa, and within order unity along the ordinate. Progress in understanding these observations has been made by expanding the domain of sigma from the critical strip, [0, 1], to the half-line [0, infinity]. The nature of the organizing principle is explained. A generic structure for strings over the expanded domain is proffered. New perspective is gained regarding the truth of the Riemann Hypothesis.