Ces\`aro average in short intervals for Goldbach numbers

TL;DR

This paper establishes an explicit formula for the Cesàro-averaged count of Goldbach representations within short intervals, advancing understanding of prime sums in number theory.

Contribution

It introduces a new explicit formula for Cesàro-averaged Goldbach representations in short intervals, extending previous results to more localized ranges.

Findings

Explicit formula for Cesàro-averaged Goldbach numbers in short intervals

Improved understanding of prime sums in localized ranges

Advancement in analytic number theory techniques

Abstract

We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals.