On Kronecker terms over global function fields

• 成果类型: Article
• 署名作者: Wei, Fu-Tsun
• 署名单位: National Tsing Hua University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00944-8
• 发表日期: 2020
• 页码: 847-907
• 关键词: limit formula; drinfeld; ELEMENTS

摘要

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}. 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.