Green's functions on Mumford curves

Fu-Tsun, Wei

Department of Mathematics

National Tsing Hua University

ftwei@math.nthu.edu.tw

    In this talk, we shall introduce an analogue of Green's function on Mumford curves. The special value of Green's function at `s=0` interprets the volume of the corresponding curve. Using harmonic analysis on Bruhat-Tits trees, we connect the derivative of Green's functions at `s=0` with the Manin-Drinfeld theta functions, which enables us to show that the special derivative here is equal to twice of the Néron's local height with sign changed.