## 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.

** Bibliography **

- Apostol: Introduction to analytic number theory. Springer
- Hardy/Wright: An introduction to the theory of numbers.
Oxford University Press
- Rose: A course in number theory.
Oxford University Press
- Hlawka/Schoißengeier/Taschner: Geometric and
analytic number theory. Springer
- Chandrasekharan: Introduction to analytic number theory.
Springer
- Edwards: Riemann's zeta function. Academic Press
- Landau: Zahlentheorie, Vol. 2. Reprint Chelsea

**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 (),
2001-02-16