Modular symbols in arithmetic progressions

par Svenja Zur Verth (EPFL, Suisse)

lundi 23 nov. 2026, 15:30 → 16:30 Europe/Paris

Salle Yvette Cauchois (IHP - Bâtiment Perrin)

Motivated by conjectures of Mazur, Rubin and Stein, the distribution of modular symbols has received a lot of attention in recent years. Notably, Petridis and Risager showed that modular symbols are asymptotically normally distributed when averaged over all denominators. A natural next step is to restrict the denominators to sparser sets, such as squarefree numbers. This requires understanding modular symbols in arithmetic progressions. Using spectral methods for Eisenstein series twisted by modular symbols, we make the dependence on the modulus explicit in the first two terms of all even moments, and in the full main term of the fourth moment. As an application, we obtain an asymptotic formula for the fourth moment over squarefree denominators.