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

doi:10.1016/j.jnt.2017.08.026

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	384-410
Number of pages	27
Journal	Journal of Number Theory
Volume	184
DOIs	https://doi.org/10.1016/j.jnt.2017.08.026
Publication status	Published - 2018 Mar

Keywords

Algebraic independence
Mahler functions
Positive characteristic

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2017.08.026

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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.",

keywords = "Algebraic independence, Mahler functions, Positive characteristic",

author = "Akinari Goto and Tanaka, {Taka aki}",

note = "Funding Information: The authors are grateful to the anonymous referee for careful reading and insightful comments that improved this paper. This work was supported by JSPS KAKENHI Grant Number 15K04792 .",

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language = "English",

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AU - Goto, Akinari

AU - Tanaka, Taka aki

N1 - Funding Information: The authors are grateful to the anonymous referee for careful reading and insightful comments that improved this paper. This work was supported by JSPS KAKENHI Grant Number 15K04792 .

PY - 2018/3

Y1 - 2018/3

N2 - 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.

AB - 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.

KW - Algebraic independence

KW - Mahler functions

KW - Positive characteristic

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SN - 0022-314X

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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