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 (Martin Raič)
Zeta I - Bohr-Jessen's Theorem, Bagchi's Theorem outside the critical strip (Miloš Puđa)
Zeta I - Bagchi's Theorem inside the critical strip (Miloš Puđa)
Zeta I - The support of Bagchi's measure (Jakob Jurij Snoj)
Zeta II - Selberg's Theorem (Marco Barbieri)
Zeta II - Dirichlet polynomial approximation, Euler product approximation (Daniel Vitas)
The Chebychev Bias - Existence of Rubinstein-Sarnak distribution (Gal Oražem)
The Chebychev Bias - The generalized simplicity hypothesis (Gal Oražem)
Exponential Sums - Distribution Theorem (Jianan Peng)
Exponential Sums - Applications
We meet on Mondays at 12-13 in classroom 3.07.
20/10/2025 Daniel Vitas: Introductory meeting [video]
03/11/2025 Martin Raič: The Erdős-Kac Theorem [video]
10/11/2025 Miloš Puđa: Zeta I - Bohr-Jessen's Theorem, Bagchi's Theorem outside the critical strip [video]
17/11/2025 Miloš Puđa: Zeta II - Bagchi's Theorem inside the critical strip [video]
24/11/2025 Jakob Jurij Snoj: Zeta I - The support of Bagchi's measure [video]
01/12/2025 Marco Barbieri: Zeta II - Selberg's Theorem [video]
08/12/2025 Daniel Vitas: Zeta II - Dirichlet polynomial approximation, Euler product approximation
15/12/2025 Gal Oražem: The Chebychev Bias - Existence of Rubinstein-Sarnak distribution
05/01/2026 Jianan Peng: Exponential Sums - Distribution Theorem