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.