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SMC Colloquium

The Sato-Tate conjecture

by Torsten Ekedahl (SU)

Europe/Stockholm
Room 14

Room 14

House 5, Kräftriket, Department of Mathematics, Stockholm University
Description

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.