Riemann's Auxiliary Function. Right limit of zeros

2024/06/11 by Juan Arias de Reyna, de Reyna, Juan Arias
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Number Theory (math.NT) #Primary 11M06 #Secondary 30D99 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.07014

openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Numerical data suggest that the zeros ρ of the auxiliary Riemann function in the upper half-plane satisfy \mathopRe(ρ)<1. We show that this is true for those zeros with \mathopIm(ρ)> 3.9211…10⁶⁵. We conjecture that this is true for all of them.

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