k 规则序列生成函数的径向拟数

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society 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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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society