# Torsten Ekedahl: The Sato-Tate conjecture

Torsten Ekedahl, SU

**Time: **Wed 2010-11-03 16.00

**Location: **Room 14, house 5, Kräftriket, Department of Mathematics, Stockholm University

The Sato-Tate conjecture is an equidistribution conjecture for certain

number-theoretically defined sequences. An example of a (generalised)

Sato-Tate conjecture is obtained by defining

$$

\sum_{n=1}^\infty \tau(n) = q\prod_{i=1}^\infty(1-q^n)^{24}.

$$

The conjecture then says that $\{\tau(n)/(2n^{5.5})\}$ is

equi-distributed with respect to a specific well-known distribution.

This is as well as the original Sato-Tate distribution has now been

proved by the combined efforts by a fairly large group of people.

I will mainly discuss how one by experimentation and

pseudo-probabilistic reasoning can arrive at the Sato-Tate conjecture

and then indicate the basic idea for the proof.