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- W4321104813 abstract "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 $a_0(z)=1$. 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 $z^gamma Q(z)$ for some explicit non-negative integer $gamma$ and such that $1/Q(z)$ is $k$-regular." @default.
- W4321104813 created "2023-02-17" @default.
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- W4321104813 date "2018-02-23" @default.
- W4321104813 modified "2023-09-28" @default.
- W4321104813 title "Becker's conjecture on Mahler functions" @default.
- W4321104813 doi "https://doi.org/10.48550/arxiv.1802.08653" @default.
- W4321104813 hasPublicationYear "2018" @default.
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