On Kronecker terms over global function fields

Fu-Tsun Wei National Tsing Hua University

Number Theory mathscidoc:1904.24002

Silver Award Paper in 2020

Inventiones mathematicae, 2020.1
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
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  • https://doi.org/10.1007/s00222-019-00944-8
  title={On Kronecker terms over global function fields},
  author={Fu-Tsun Wei},
  booktitle={Inventiones mathematicae},
Fu-Tsun Wei. On Kronecker terms over global function fields. 2020. In Inventiones mathematicae. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190430211821082424307.
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