#### Chandrasekhar Hall

#### Probabilistic Number Theory

#### J-M. Deshouillers

##### University of Bordeaux

*The course, which is introductory, can be followed by graduate *

students or more advanced persons.

The afternoon courses will be

self-contained:

new concepts will be

introduced during the morning tutorials.

The first lecture will be presented as a colloquium talk

with a slightly broader scope:

interactions between probability theory and number theory.

The other lectures

will be organized according to the following pattern:

1. Arithmetical functions: basic notions.

Probability: basic notions.

2. Distribution functions of arithmetical functions.

Weak convergence of random variables.

The Turan-Kubilius inequality.

3. Arithmetical functions and probabilistic models:

A weak version of the Erd\H{o}s-Kac Theorem;

a stronger form of the Hardy-Ramanujan Theorem.

The Erdos-Wintner theorem.

4. Additive number theory: basic notions.

Erdos approach to additive questionsvia probability theory.

A problem of Sidon.

The Erdos-Renyi model for $s$-th powers.

5. Arithmetico-probabilist models.

Atkin's approximation of sums of two squares.

An arithmetical Erdos-Renyi model.

Vu's economical bases formed with $s$-th powers.

Done