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.

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Correspondence to Claus Bauer.

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Bauer, C. Large sieve inequality with sparse sets of moduli applied to Goldbach conjecture. Front. Math. China 12, 261–280 (2017). https://doi.org/10.1007/s11464-016-0527-x

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Keywords

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

MSC

  • 11F32
  • 11F25