Kronecker limit formula over function fields


Fu-Tsun Wei

13:30:00 - 14:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will introduce a "non-holomorphic" Eisenstein series on the Drinfeld half space (of arbitrary rank), and discuss its analytic properties. From an explicit expression of the meromorphic continuation of this Eisenstein series, we are able to determine all the derivatives at the special point s=0. This is similar to the formula of the Stieltjes constants occurring in the Laurent expansion of the Riemann zeta function at s = 1. Consequently, we obtain an analogue of Kronecker limit formula for the the Eisenstein series in question. As an application, a Colmez-type formula for "CM" Drinfeld modules is carried out. Finally, our Kronecker limit formula allows us to express the first derivative of Jacquet-Shalika Eisenstein series at s=0 in terms of "Drinfeld-Siegel" units.