### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

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## 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