On the Brun-Titchmarsh theorem
On the Brun-Titchmarsh theorem
MIKAWA 1. Introduction.Let $\pi(x;q, a)$ denote the number of primes not exceeding $x$ and being congruent to $a$ modulo $q$ .In 1936 P. Tur\'an [6] showed that, under the ex- tended Riemann hypothesis, $\pi(x;q, a)\sim\frac{x}{\varphi(q)\log x}$ as $ x\rightarrow\infty$ for all $q\leqq x(\log x)^{-2-\epsilon}(\epsilon>0)$ and almost-all reduced residue classes $a$ …