MathSciDoc: An Archive for Mathematician ∫

We establish a general Kronecker limit formula of arbitrary rank over global function fields with Drinfeld period domains playing the role of upper-half plane. The Drinfeld-Siegel units come up as equal characteristic modular forms replacing the classical $\Delta$. This leads to analytic means of deriving a Colmez-type formula for "stable Taguchi height" of CM Drinfeld modules having arbitrary rank. A Lerch-Type formula for "totally real" function fields is also obtained, with the Heegner cycle on the Bruhat-Tits buildings intervene. Also our limit formula is naturally applied to the special values of both the Rankin-Selberg L-functions and the Godement-Jacquet L-functions associated to automorphic cuspidal representations over global function fields.

Function field, Drinfeld period domain, Bruhat-Tits building, Kronecker limit formula, Drinfeld-Siegel unit, Mirabolic Eisenstein series, CM Drinfeld module, Taguchi height, Colmez-type fomula, Special L-value