函数场中乘法函数的相关性

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2022-12-10 DOI:10.1112/mtk.12181

Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen

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引用次数: 4

摘要

我们开发了一种研究特征和的方法，通过乘法函数f:Fq[t]进行加权→S1$f\colon\mathbb{F}_q[t] \rightarrow S^1$，形式为∑deg（G）=NGmonif（G）x2（G）ξ（G{F}_q[t] $。然后，我们在函数域Fq[t]$\mathbb上推导出Matomäki–Radziwiłł{F}_q[t] $，其中q是固定的。前者改进了Gorodetsky的工作，后者扩展了Sawin–Shusterman关于Möbius函数对各种q值的相关性的工作。与整数设置相比，我们遇到了不同的现象，特别是在q是2的幂的情况下的低特征问题。作为我们结果的一个应用，我们给出了Kátai关于小增量乘法函数分类的猜想的函数域版本的简短证明，所获得的分类和证明不同于整数情况下的现有分类和证明。在一篇配套论文中，我们使用这些结果来刻画函数域中乘法函数的部分和的极限行为，特别是解决Fq[t]$\mathbb上Erdõs差异问题的“校正”形式{F}_q[t] $。

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Correlations of multiplicative functions in function fields

We develop an approach to study character sums, weighted by a multiplicative function $f : F_{q} [t] \to S^{1}$ , of the form

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.