Large sieve inequality with sparse sets of moduli applied to Goldbach conjecture

Abstract

We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic progressions.

Keywords

Three primes theorem / exponential sums over primes / sparse set of modules

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg