Becker’s conjecture on Mahler functions

Title: Becker’s conjecture on Mahler functions
Creator: Bell, Jason P.; Chyzak, Frédéric; Coons, Michael; Dumas, Philippe
Relation: Transactions of the American Mathematical Society Vol. 372, Issue 5, p. 3405-3423
Publisher Link: http://dx.doi.org/10.1090/tran/7762
Publisher: American Mathematical Society
Resource Type: journal article
Date: 2019
Description: In 1994, Becker conjectured that if F(z) is a k-regular power series, then there exists a k-regular rational function R(z) such that F(z)/R(z) satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies a0(z) = 1. In this paper, we prove Becker’s conjecture in the best-possible form; we show that the rational function R(z) can be taken to be a polynomial zγQ(z) for some explicit non-negative integer γ and such that 1/Q(z) is k-regular.
Subject: Mahler functions; polynomials; rational functions; functional equations
Identifier: http://hdl.handle.net/1959.13/1509111
Identifier: uon:56199
Identifier: ISSN:0002-9947
Language: eng
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