On the real projection of the zeros of 1+2^s+...+n^s

2011/02/14 by Eric Dubon, Gaspar Mora, Dubon, Eric +10
Mathematics · #Analytic Number Theory Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CV

paper · pdf · doi:10.48550/arxiv.1102.2767

26 pages

arxiv created 2011/02/14 · openalex publication_date 2011/02/14 · arxiv updated 2011/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we focus on the existence of accumulation points of the subset defined by the real projection of the zeros of the partial sums of the Riemann zeta functions. That would imply the existence of an infinite amount of zeros of the partial sums of the Riemann zeta functions arbitrarily close to a line parallel to the imaginary axis passing through every accumulation point.

Related

• Accumulation points of the sets of real parts of zeros of the partial sums of the Riemann zeta function
• Zeros of the Riemann Zeta Function
• The real parts of the nontrivial Riemann zeta function zeros
• Zeros of partial sums of the Riemann zeta-function
• Disproof of the Riemann Hypothesis