# Journal of the Ramanujan Mathematical Society

Volume 36, Issue 4, December 2021 pp. 339–352.

An M-function associated with Goldbach's problem

**Authors**:
Kohji Matsumoto

**Author institution:**K. Matsumoto: Graduate School of Mathematics, Nagoya University,
Chikusa-ku, Nagoya 464 8602, Japan

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

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