English

Explicit formulae for averages of Goldbach representations

Number Theory 2019-09-25 v1

Abstract

We prove an explicit formula, analogous to the classical explicit formula for ψ(x)\psi(x), for the Ces\`aro-Riesz mean of any order k>0k>0 of the number of representations of nn as a sum of two primes. Our approach is based on a double Mellin transform and the analytic continuation of certain functions arising therein.

Keywords

Cite

@article{arxiv.1712.00737,
  title  = {Explicit formulae for averages of Goldbach representations},
  author = {J. Brüdern and J. Kaczorowski and A. Perelli},
  journal= {arXiv preprint arXiv:1712.00737},
  year   = {2019}
}

Comments

16 pages

R2 v1 2026-06-22T23:04:52.642Z