Translator Disclaimer
June 2014 Arithmetic Properties of Solutions of Certain Functional Equations with Transformations Represented by Matrices Including a Negative Entry
Taka-aki TANAKA
Tokyo J. Math. 37(1): 211-223 (June 2014). DOI: 10.3836/tjm/1406552440

Abstract

Mahler's method gives algebraic independence results for the values of functions of several variables satisfying certain functional equations under the transformations of the variables represented as a kind of the multiplicative action of matrices with integral entries. In the Mahler's method, the entries of those matrices must be nonnegative; however, in the special case stated in this paper, one can admit those matrices to have a negative entry. We show the algebraic independence of the values of certain functions satisfying functional equations under the transformation represented by such matrices, expressing those values as linear combinations of the values of ordinary Mahler functions.

Citation

Download Citation

Taka-aki TANAKA. "Arithmetic Properties of Solutions of Certain Functional Equations with Transformations Represented by Matrices Including a Negative Entry." Tokyo J. Math. 37 (1) 211 - 223, June 2014. https://doi.org/10.3836/tjm/1406552440

Information

Published: June 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1303.11083
MathSciNet: MR3264523
Digital Object Identifier: 10.3836/tjm/1406552440

Subjects:
Primary: 11J85
Secondary: 11B39

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.37 • No. 1 • June 2014
Back to Top