Sums of many primes

TL;DR

Under the assumption of GRH, the paper derives an explicit formula for counting representations of integers as sums of at least five primes, improving error estimates over previous results.

Contribution

The paper provides a new explicit formula for prime sum representations under GRH with improved error bounds compared to prior work.

Findings

Explicit formula for prime sum representations under GRH

Enhanced error estimates with logarithmic improvements

Applicable for sums of five or more primes

Abstract

Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors an analogous result by Friedlander-Goldston.