Arithmetic of L-values and various dynamics behind it

Abstract

In the talk, I am going to review previous works on the arithmetic of special values of various twisted L-functions at critical points. Among interesting stories, main emphasis will be put on non-vanishing modulo prime of the special L-values. Ever since the simplest case, namely Dirichlet L-values in Iwasawa theoretic setting, was successfully resolved by Ferrero-Washington in 1979, many researchers have observed that dynamical phenomena play crucial roles in several studies on the topic. Some of the phenomena are roughly generalizations of Kronecker's theorem on equi-distribution statement for (p-adic) normal numbers. In the latter part of the talk, I will introduce relevant works or on-going researches of mine that are joint works with B. Jun, J. Lee, M. Kim, and A. Burungale.