### 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 |
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Journal | Journal of Number Theory |

DOIs | |

Publication status | Accepted/In press - 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*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.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - 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

AU - Goto, Akinari

AU - Tanaka, Takaaki

PY - 2017

Y1 - 2017

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

KW - Primary

KW - Secondary

UR - http://www.scopus.com/inward/record.url?scp=85030461242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030461242&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2017.08.026

DO - 10.1016/j.jnt.2017.08.026

M3 - Article

AN - SCOPUS:85030461242

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -