English

Mahler equations and rationality

Classical Analysis and ODEs 2017-03-27 v2

Abstract

We give another proof of a result of Adamczewski and Bell concerning Mahler equations: A formal power series satisfying a pp- and a qq-Mahler equation over C(x){\mathbb C}(x) with multiplicatively independent positive integers pp and qq 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.

Keywords

Cite

@article{arxiv.1605.08830,
  title  = {Mahler equations and rationality},
  author = {Reinhard Schäfke and Michael F. Singer},
  journal= {arXiv preprint arXiv:1605.08830},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T14:11:46.274Z