k 规则序列生成函数的径向拟数

Pub Date : 2024-09-13 DOI:10.1017/s0004972724000480

MICHAEL COONS, JOHN LIND

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引用次数: 0

摘要

我们给出了贝尔和库恩斯定理的新证明['马勒函数的超越性检验'，Proc.Amer.Math.145(3)（2017），1061-1070]关于作为正则序列生成函数的马勒函数的前阶径向渐近性的新证明。我们的方法允许我们对贝尔和库恩斯证明存在的振荡进行描述。这扩展了 Poulet 和 Rivoal 的最新成果['马勒函数的径向行为'，《国际数论杂志》，待出版]。

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RADIAL ASYMPTOTICS OF GENERATING FUNCTIONS OF k-REGULAR SEQUENCES

We give a new proof of a theorem of Bell and Coons [‘Transcendence tests for Mahler functions’, Proc. Amer. Math. Soc. 145(3) (2017), 1061–1070] on the leading order radial asymptotics of Mahler functions that are the generating functions of regular sequences. Our method allows us to provide a description of the oscillations whose existence was shown by Bell and Coons. This extends very recent results of Poulet and Rivoal [‘Radial behavior of Mahler functions’, Int. J. Number Theory, to appear].

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