@article{ef2fe6dd02d548a591470d91549bc229,
title = "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 = "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 . Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",
year = "2018",
month = mar,
doi = "10.1016/j.jnt.2017.08.026",
language = "English",
volume = "184",
pages = "384--410",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
}