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

Chieh Yu Chang, Ahmad ElGuindy, Matthew A. Papanikolas

Research output: Contribution to journalArticle

Abstract

We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring Fq[θ]. This generalizes results of Anderson for the rank 1 case. As an application we show that certain special values of Goss L-functions are linear forms in Drinfeld logarithms and are transcendental.

Original languageEnglish
Pages (from-to)125-144
Number of pages20
JournalJournal of the London Mathematical Society
Volume97
Issue number2
DOIs
Publication statusPublished - 1 Apr 2018

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Drinfeld Modules
Linear Forms
Transcendental
Polynomial ring
L-function
Logarithm
Generalise
Arbitrary
Theorem

Keywords

  • 11G09 (primary)
  • 11J93 (secondary)
  • 11M38

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Log-algebraic identities on Drinfeld modules and special L-values. / Chang, Chieh Yu; ElGuindy, Ahmad; Papanikolas, Matthew A.

In: Journal of the London Mathematical Society, Vol. 97, No. 2, 01.04.2018, p. 125-144.

Research output: Contribution to journalArticle

Chang, Chieh Yu ; ElGuindy, Ahmad ; Papanikolas, Matthew A. / Log-algebraic identities on Drinfeld modules and special L-values. In: Journal of the London Mathematical Society. 2018 ; Vol. 97, No. 2. pp. 125-144.
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