On Kronecker terms over global function fields

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.