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 | |
Publication status | Published - 2018 Mar |
Keywords
- Algebraic independence
- Mahler functions
- Positive characteristic
ASJC Scopus subject areas
- Algebra and Number Theory