Sums of many primes (Q413423)

Under the Generalized Riemann Hypothesis, the authors establish an explicit formula for the number of representations of an integer as a sum of \(k \geq 5\) primes. The explicit formula has the expected main term, a secondary main term depending on the zeros of \(L\)-functions, and an error term of smaller order of magnitude.NEWLINENEWLINEBy applying the version of the circle method originally introduced by Hardy and Littlewood, involving series rather than truncated sums, the authors improve previous results on the error terms by some logarithmic factors.