Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field

Akinari Goto, Taka aki Tanaka

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1 Citation (Scopus)

Abstract

We give positive characteristic analogues of complex entire functions having remarkable property that their values as well as their derivatives of any order at any nonzero algebraic numbers are algebraically independent. These results are obtained by establishing a criterion for the algebraic independence of the values of Mahler functions as well as that of the algebraic independence of the Mahler functions themselves over any function fields of positive characteristic.

Original languageEnglish
Pages (from-to)384-410
Number of pages27
JournalJournal of Number Theory
Volume184
DOIs
Publication statusPublished - 2018 Mar

Keywords

  • Algebraic independence
  • Mahler functions
  • Positive characteristic

ASJC Scopus subject areas

  • Algebra and Number Theory

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