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 , for the Ces\`aro-Riesz mean of any order of the number of representations of 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