Mahler equations and rationality

Abstract

We give another proof of a result of Adamczewski and Bell concerning Mahler equations: A formal power series satisfying a $p-$ and a $q-$Mahler equation over $\mathbb{C}(x)$ with multiplicatively independent positive integers $p$ and $q$ is a rational function. The proof presented here is self-contained and is essentially a compilation of proofs contained in the recent preprint "Consistent systems of linear differential and difference equations", arXiv:1605.02616 [math.CA], by the same authors.

arXiv admin note: text overlap with arXiv:1605.02616 A few grammatical/typographical changes and text added to clarify the proofs of Lemmas 4 and 8

References in corpus (2)

• The rational-transcendental dichotomy of Mahler functions
• A problem around Mahler functions

Cited by in corpus (1)

• Mahler's method in several variables II: Applications to base change problems and finite automata