Morten Risager (U Kopenhagen)
Tuesday, December 12, 2017 - 13:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, 006, Haus 3, Erdgeschoss
Forschungsseminar Arithmetische Geometrie
Prof. Jürg Kramer / Prof. Thomas Krämer
Mazur, Rubin, and Stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve L-functions. Two of these conjectures relate to the asymptotic growth of the first and second moments of the modular symbols. We prove these on average by using analytic properties of Eisenstein series twisted by modular symbols. Another of their conjectures predicts the Gaussian distribution of normalized modular symbols. We prove a refined version of this conjecture.
submitted by Marion Thomma (thomma@math.hu-berlin.de, 2093-5815)