Monday, January 15 2018 - Friday, January 19 2018
15:30 - 17:00

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
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.

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