Number Theory Seminar

Mazur-Rubin proposed several conjectures on the distribution of modular symbols. In 2017, Petridis and Risager successfully gave a proof for an average version using a sophisticated theory on Eisenstein series twisted by moments of modular symbols. In the talk, I will present another proof of the average version including results on residual equi-distribution of the symbols, using the spectral properties of a transfer operator associated to a skewed Gauss map. This is joint work with Jungwon Lee.