SPEAKER:     Hae-Sang Sun

TITLE:    Rational Function Measure and Non-vanishing mod $p$ of $L$-values

ABSTRACT:

We will first briefly review Washington's classical result on the non-vanishing mod $p$ of $L$-values and discuss the totally real field case. After introducing a measure on the $\ell$-adic completion of the integer ring of the totally real field defined by a rational function on tori and relating it to special $L$-values, we will define some Hecke operator acting on the rational function and discuss some geometric properties.