On Kronecker terms over global function fields

2018/02/20 by Wei, Fu-Tsun · 1 citation
#11G09 #11M36 #11R58 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.06987

Abstract

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 Δ. 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.

Cited by

• On special values of meromorphic Drinfeld modular forms of arbitrary rank at CM points

Related

• Several-variable Kronecker limit formula over global function fields
• Quadratic Euler-Kronecker constants in positive characteristic
• La formule limite de Kronecker
• On Drinfeld modular forms of higher rank and quasi-periodic functions
• The refined class number formula for Drinfeld modules