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, Takaaki Tanaka

Research output: Contribution to journalArticle

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
JournalJournal of Number Theory
DOIs
Publication statusAccepted/In press - 2017

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Algebraic Independence
Relatively prime
Positive Characteristic
Functional equation
Algebraic number
Complex Functions
Function Fields
Entire Function
Analogue
Derivative

Keywords

  • Algebraic independence
  • Mahler functions
  • Positive characteristic
  • Primary
  • Secondary

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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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.",
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