Analytic Number Theory

Course (4 hours weekly + 2 hours Problem sessions) by O. Forster
Winter Semester 2001/02, Department of Mathematics, LMU München

Time and Room: Mon 9-11 HS 132, Wed 11-13 E27
Starts on Monday, Oct. 15, 2001, at 9:15h

Problem sessions: Mo 14-16, HS 132

What this course is about: One of the classical problems in number theory is the distribution of primes. In analytic number theory one uses the theory of analytic functions to attack this and other problems. In this course, we will (among other things) give a proof of the Prime Number Theorem, asserting that the number of primes less than or equal to a bound X is asymptotically equal to X/log(X) as X tends to infinity. The proof uses the Riemann zeta function. We will also explain the famous Riemann Hypothesis about the zeroes of the zeta function (this is one of the Millennium Problems, worth $ 1 million, if you can solve it). Another theme is Dirichlet's theorem on primes in arithmetic progressions, where so called L-functions are used.

Prerequisites: Elements of the theory of analytic functions, including residue calculus.


Lecture notes

This course will be followed by a course in Algorithmic Number Theory (SS 2002) and one in Cryptography (WS 2002/03).
Topics for master theses (and diploma theses) will be available from these subjects.
Otto Forster (email), 2001-02-16