The course is devoted to the advanced study of the sieve method, one of the most powerful methods in analytic number theory. The main purpose of the course is to teach the students to apply different sieve methods (Selberg sieve, linear sieve etc.) together with some other additional tools based on the estimates of Kloosterman sums etc. The course is organized in the form of detailed analysis of the solutions of the most typical problems, that have been solved earlier by C.Hooley, namely the below estimate of the largest prime divisor of the numbers $n^2+1, n\le x$, the estimation of the prime-counting function $\pi(x;q,a)$ for almost all modules $q$ etc.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Lecturer
Korolev Maxim Aleksandrovich

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center