[NTNU Number Theory Seminar] 【March 7】Fu-Tsun Wei / Several-variable Kronecker limit formula over function fields.

In this talk, I will present a Kronecker-type limit formula for several-variable Eisenstein series over function fields. The main theorem expresses the derivatives of these Eisenstein series as averaged integrals of certain period quantities along the associated “Heegner cycles” on Drinfeld modular varieties. A key innovation lies in our use of the Berkovich analytic structure of the Drinfeld period domains, which enables the parametrization of the Heegner cycles in question by Euclidean “parallelepiped” regions. Consequently, we apply the formula to provide period interpretations of the “Kronecker terms” of Dedekind–Weil zeta functions and Dirichlet L-functions associated with ring and ray class characters.