Jan-Hendrik Evertse (UL), Adelina Manzateanu (UL)
Basic algebra, basic complex analysis. Everything which is needed is contained in Chapter 0 of the lecture notes and can be read by the students prior to the course. Chapter 0 and some other parts of the lecture notes can be found on the analytic number theory website http://pub.math.leidenuniv.nl/~evertsejh/ant-mastermath.html
Precorded lectures can be found on VIMEO, https://vimeo.com/showcase/7526643
password Js0V (capital J, lower case s, zero, captial V)
Aim of the course
The aim of the course will be to learn the students some basics of analytic number theory, focused on prime number theory. In addition we will discuss an application of the circle method.
A short overview of the contents:
The first part (taught by Jan-Hendrik Evertse) will be on prime number theory. Topics to be discussed are Dirichlet series, arithmetic functions, characters, the Riemann zeta function and L-functions, a Tauberian theorem, finally leading to a proof of the prime number theorem for arithmetic progressions. The second part (taught by Adelina Manzateanu) will consist of a description of the Hardy-Littlewood circle method. As an application it will be shown that every sufficiently large integer is the sum of nine positive cubes.