On simultaneous approximation of the values of certain Mahler functions
Keijo V\"a\"an\"anen, Wen Wu
TL;DR
This paper develops a method to estimate how well certain Mahler functions' values can be simultaneously approximated, using Hermite-Padé approximations and functional equations to generate and analyze sequences of approximations.
Contribution
The paper introduces a novel approach combining Hermite-Padé approximations with functional equations to estimate simultaneous approximation exponents of Mahler functions.
Findings
Derived bounds for approximation exponents of specific Mahler functions
Constructed infinite sequences of approximations using functional equations
Applied numerical methods to validate theoretical estimates
Abstract
In this paper, we estimate the simultaneous approximation exponents of the values of certain Mahler functions. For this we construct Hermite-Pad\'{e} approximations of the functions under consideration, then apply the functional equations to get an infinite sequence of approximations and use the numerical approximations obtained from this sequence.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Approximation Theory and Sequence Spaces · Mathematical functions and polynomials