A partial Bombieri-Vinogradov theorem with explicit constants. (English) Zbl 1440.11181

Sedunova, Alisa

Algèbre et thèorie des nombres 2018. Besançon: Presses Universitaires de Franche-Comté. Publ. Math. Besançon, Algèbre Théor. Nombres 2018, 101-110 (2018).

Summary: In this paper we improve the result of [A. Akbary and K. Hambrook, Math. Comput. 84, No. 294, 1901–1932 (2015; Zbl 1341.11053)] with getting \((\log x)^{\frac72}\) instead of \((\log x)^{\frac92}\). In particular we obtain a better version of Vaughan’s inequality by applying the explicit variant of an inequality connected to the Möbius function from [H. A. Helfgott, in: Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa. 391–418 (2014; Zbl 1373.11074)].
For the entire collection see [Zbl 1398.14001].

MSC:

11N13	Primes in congruence classes
11N05	Distribution of primes
11N36	Applications of sieve methods

Keywords:

primes in arithmetic progression; Bombieri-Vinogradov theorem; large sieve

Citations:

Zbl 1341.11053; Zbl 1373.11074