A mean-square value of the Riemann zeta function over an arithmetic progression

2022/12/13 by Hirotaka Kobayashi, Kobayashi, Hirotaka
Mathematics · #Algebraic and Geometric Analysis #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.06520

openalex publication_date 2022/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an asymptotic formula for the second discrete moment of the Riemann zeta function over the arithmetic progression (1)/(2) + in. It shows that the first main term is equal to that of the continuous mean value.

Related

• Mean-square values of the Riemann zeta function on arithmetic progressions
• The Riemann-zeta function on vertical arithmetic progressions
• Discrete Moments of the Riemann Zeta-Function near σ=1
• A note on the mean square of the Riemann zeta-function
• A discrete mean value of the derivative of the Riemann zeta function