Kronecker limit formula over global function fields

Fu-Tsun Wei National Central University

Number Theory mathscidoc:1611.24006

Distinguished Paper Award in 2019

American Journal of Mathematics, 139, (4), 1047-1084, 2017
The aim of this paper is to present a function field analogue of the classical Kronecker limit formula. We first introduce a “non-holomorphic” Eisenstein series on the Drinfeld half plane, and connect its “second term” with Gekeler’s discriminant function. One application is to express the Taguchi height of rank 2 Drinfeld modules with complex multiplication in terms of the logarithmic derivative of the corresponding zeta functions. Moreover, from the integral form of the Rankin-type L-function associated to two “Drinfeld-type” newforms, we then derive a formula for a non-central special derivative of the L-function in question. Adapting the classical approach, we also obtain a Kronecker-type solution for Pell’s equation over function fields.
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@inproceedings{fu-tsun2017kronecker,
  title={Kronecker limit formula over global function fields},
  author={Fu-Tsun Wei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161114231443922765618},
  booktitle={American Journal of Mathematics},
  volume={139},
  number={4},
  pages={1047-1084},
  year={2017},
}
Fu-Tsun Wei. Kronecker limit formula over global function fields. 2017. Vol. 139. In American Journal of Mathematics. pp.1047-1084. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161114231443922765618.
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