残差类环中的位数和函数

IF 0.6 3区数学 Q3 MATHEMATICS

Periodica Mathematica Hungarica Pub Date : 2024-07-02 DOI:10.1007/s10998-024-00595-0

Huaning Liu, Zehua Liu

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引用次数: 0

摘要

Dartyge 和 Sárközy 引入了有限域中数位的概念，并研究了具有固定数位和的\({\mathbb {F}}_q\) 的多项式值的性质。斯韦内普尔（Swaenepoel）提供了对\({\mathbb {F}}_q\) 的特殊序列的元素数的精确估计，这些序列的数位之和是规定的。在本文中，我们研究了残差类环中的位数和函数，并通过使用对特征和及指数和 modulo 素幂的估计，给出了一些渐近公式和精确等式。

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The sum-of-digits function in rings of residue classes

Dartyge and Sárközy introduced the notion of digits in finite fields and studied the properties of polynomial values of \({\mathbb {F}}_q\) with a fixed sum of digits. Swaenepoel provided sharp estimates for the number of elements of special sequences of \({\mathbb {F}}_q\) whose sum of digits is prescribed. In this paper we study the sum-of-digits function in rings of residue classes and give a few asymptotic formulas and exact identities by using estimates for character sums and exponential sums modulo prime powers.

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来源期刊

Periodica Mathematica Hungarica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.