We prove an explicit formula, analogous to the classical explicit formula for $psi(x)$, for the Cesaro-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.
Explicit formulae for averages of Goldbach representations
PERELLI, A.
2019-01-01
Abstract
We prove an explicit formula, analogous to the classical explicit formula for $psi(x)$, for the Cesaro-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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