Abstract:

The celebrated Kronecker limit formula expresses the "second term" of non-holomorphic Eisenstein series in terms of Siegel modular units on the complex upper half plane. This formula enables us to gain geometric means of various special L-values, which provides significant evidences for the Colmez conjecture and the Beilinson program. In this talk, I will discuss this phenomenon in the function field setting, and explore the arithmetic of "Kronecker terms" over function fields.