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

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, Takaaki Tanaka

Department of Mathematics

Research output: Contribution to journal › Article

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
Journal	Journal of Number Theory
DOIs	https://doi.org/10.1016/j.jnt.2017.08.026
Publication status	Accepted/In press - 2017

Fingerprint

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

Goto, A., & Tanaka, T. (Accepted/In press). 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. Journal of Number Theory. https://doi.org/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. / Goto, Akinari; Tanaka, Takaaki.

In: Journal of Number Theory, 2017.

Research output: Contribution to journal › Article

Goto, A & Tanaka, T 2017, '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', Journal of Number Theory. https://doi.org/10.1016/j.jnt.2017.08.026

Goto A, Tanaka T. 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. Journal of Number Theory. 2017. https://doi.org/10.1016/j.jnt.2017.08.026

Goto, Akinari ; Tanaka, Takaaki. / 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. In: Journal of Number Theory. 2017.

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Access to Document

10.1016/j.jnt.2017.08.026