- 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
- Reviewed
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