On the Riemann Zeta Function and the fractional part of rational powers

2018/08/20 by Tal Barnea, Barnea, Tal
Mathematics · Physics and Astronomy · #11A55 11M99 11Y65 11K31 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #math.NT #msc:11A55 #msc:11K31 #msc:11M99 #msc:11Y65

paper · pdf · doi:10.48550/arxiv.1808.06653

openalex publication_date 2018/08/20 · arxiv created 2018/09/15 · arxiv updated 2018/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta Function.

Related

• Fractional Parts and their Relations to the Values of the Riemann Zeta Function
• A Proof of the Riemann Hypothesis and Determination of the Relationship Between Non- Trivial Zeros of Zeta Functions and Prime Numbers
• On the prime zeta function and the Riemann hypothesis
• New results based on Riemann hypothesis is tenable
• A simple reformulation of Riemann Zeta function