An M-function associated with Goldbach's problem

TL;DR

This paper introduces the M-function, a new mathematical tool that helps describe the distribution of values related to Goldbach's problem, providing a limit theorem for its main term.

Contribution

The paper establishes the existence of the M-function and formulates a limit theorem for the value-distribution in Goldbach's problem, advancing understanding of its asymptotic behavior.

Findings

Existence of the M-function proven

Limit theorem for the main term established

Provides new insights into Goldbach's problem

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.