[GS_M_NT] Non-vanishing mod $p$ of Hecke $L$-values and abelian modular symbols over real quadratic fields.
ABSTRACT
Non-vanishing mod $p$ of $L$-values of $\ell$-adic families has been widely studied by many researchers. One of the famous results is Washington's celebrated theorem published in 1978. In 2007, Sun reproved this result by studying the distribution of abelian modular symbols on the cylinder over the rational number field. In this talk, I will introduce a notion of cylinder over real quadratic fields and abelian modular symbols on it. Also, I will suggest a generalization of Washington 1978. This work is an ongoing research and joint with Hae-Sang Sun.