Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the Brun-Titchmarsh theorem

100%

Maynard J.

Acta Arithmetica

2013

tom 157

nr 3

249-296

The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(ϕ(q)logx) for some value C depending on logx/logq. Different authors have provided different estimates for C in different ranges for logx/logq, all of which give C>2 when logx/logq is bounded. We show that one can take C=2 provided that logx/logq ≥ 8 and q is sufficiently large. Moreover, we also produce a lower bound of size $x/(q^{1/2}ϕ(q))$ when logx/logq ≥ 8 and is bounded. Both of these bounds are essentially best-possible without any improvement on the Siegel zero problem.

Ograniczanie wyników

1 Acta Arithmetica

1 Maynard J.

1 2013

Wyniki wyszukiwania

On the Brun-Titchmarsh theorem