This is the website for the reading group on Probabilistic Number Theorey that we are holding in the Winter semester 2025/26 in Ljubljana.
The main reference is the book An introduction to probabilistic number theory by Emmanuel Kowalski.
Each participant chooses a topic and prepares a one hour lecture for the group. You do not need to cover the entire material in great detail and it is perfectly fine to focus on explaining the main ideas.
If you decide to participate, please send an email to urban.jezernik@fmf.uni-lj.si so I can mark the topic as chosen.
A list of topics, along with references, is available here (prepared by Daniel Vitas).
The Erdős-Kac Theorem
Zeta I - Bohr-Jessen's Theorem, Bagchi's Theorem outside the critical strip
Zeta I - Bagchi's Theorem inside the critical strip
Zeta I - The support of Bagchi's measure
Zeta II - Selberg's Theorem
Zeta II - Dirichlet polynomial approximation, Euler product approximation
The Chebychev Bias - Existence of Rubinstein-Sarnak distribution
The Chebychev Bias - The generalized simplicity hypothesis
Exponential Sums - Distribution Theorem
Exponential Sums - Applications
We meet on Mondays at 12-13 in classroom 3.07.
20/10/2025 Daniel Vitas: Introductory meeting