Log-algebraic identities on Drinfeld modules and special L-values

Chieh-Yu Chang National Tsing Hua University Ahmad El-Guindy Texas A&M University in Qatar Matthew A. Papanikolas Texas A&M University

Number Theory mathscidoc:1703.24019

We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules de ned over the polynomial ring Fq[\theta]. This generalizes results of Anderson for the rank one case. As an application we show that certain special values of Goss L-functions are linear forms in Drinfeld logarithms and are transcendental.
Drinfeld modules; log-algebraicity; Taelman's formula; Goss L-functions
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@inproceedings{chieh-yulog-algebraic,
  title={Log-algebraic identities on Drinfeld modules and special L-values},
  author={Chieh-Yu Chang, Ahmad El-Guindy, and Matthew A. Papanikolas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170323152207644023733},
}
Chieh-Yu Chang, Ahmad El-Guindy, and Matthew A. Papanikolas. Log-algebraic identities on Drinfeld modules and special L-values. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170323152207644023733.
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