An M-function associated with Goldbach's problem

2021/01/19 by Kohji Matsumoto, Matsumoto, Kohji
Mathematics · #11M26 #11M41 #11M99 #11P32 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2101.07446

openalex publication_date 2021/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of the M-function, by which we can state the limit theorem for the value-distribution of the main term in the asymptotic formula for the summatory function of the Goldbach generating function.

Citations

• On the value-distribution of symmetric power L-functions

Related

• M-functions and screw functions originating from Goldbach's problem and zeros of the Riemann zeta function
• Explicit estimates for the Goldbach summatory function
• Explicit formula for the average of Goldbach and prime tuples representations
• The asymptotic formula in the Goldbach binary problem
• Goldbach's Conjecture and Euler's ϕ-Function