Trivial zeros of Riemann auxiliary function

2024/06/14 by Juan Arias de Reyna, de Reyna, Juan Arias
Mathematics · #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Primary 11M06 #Secondary 30D99

paper · pdf · doi:10.48550/arxiv.2406.09796

openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that s=-2n is a simple zero of \mathop\mathcal R(s) for each integer n≥1. Here \mathop\mathcal R(s) is the function found by Siegel in Riemann's posthumous papers.

Related

• On Siegel results about the zeros of the auxiliary function of Riemann
• Statistic of zeros of Riemann auxiliary function
• Riemann's Auxiliary Function. Right limit of zeros
• Regions without zeros for the auxiliary function of Riemann
• Report on some papers related to the function \mathop\mathcal R (s) found by Siegel in Riemann's posthumous papers