<POSTECH PMI Number Theory Seminar>

Title: Genus character L-functions and their applications

Abstract: We introduce the general genus character for two distinct (not necessarily relatively prime) discriminants of quadratic fields. We provide an explicit formula for the genus character L-function of a quadratic order, along with two different proofs. As applications, we generalize the Hirzebruch-Zagier formula for the class numbers of imaginary quadratic fields and investigate congruences between Hirzebruch sums and class numbers modulo powers of two. This is joint work with Yoshinori Mizuno.