Dynamics of continued fractions and conjecture of Mazur-Rubin

Abstract: Mazur and Rubin established several conjectural statistics for modular symbols. We show that the conjecture holds on average. We plan to introduce the approach based on spectral analysis of transfer operator associated to a certain skew-product Gauss map and consequent result on mod p non-vanishing of modular L-values with Dirichlet twists (joint with Hae-Sang Sun).

number theory

Audience: researchers in the topic

NCTS Number Theory Seminar