Goldbach Representations in Arithmetic Progressions and zeros of Dirichlet L-functions

Gautami Bhowmik, Karin Halupczok, Kohji Matsumoto, Yuta Suzuki

Published 2017-04-20Version 1

Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression. On the other hand the existence of good error terms gives information on the the location of zero free regions of L-functions and possible Siegel zeros. Similar results are obtained for an integer in a congruence class expressed as the sum of two primes.