Explicit formulae for averages of Goldbach representations

J. Brüdern; J. Kaczorowski; A. Perelli

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arXiv · 1712.00737

Explicit formulae for averages of Goldbach representations

J. Brüdern·J. Kaczorowski·A. Perelli

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Abstract

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

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BibTeX RIS

J. Brüdern, J. Kaczorowski, A. Perelli. 2017-12-03. Explicit formulae for averages of Goldbach representations. https://arxiv.org/abs/1712.00737

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