Functional graphs of families of quadratic polynomials

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2022-08-03 DOI:10.1090/mcom/3838

B. Mans, M. Sha, I. Shparlinski, Daniel Sutantyo

引用次数: 1

Abstract

We study functional graphs generated by several quadratic polynomials, acting simultaneously on a finite field of odd characteristic. We obtain several results about the number of leaves in such graphs. In particular, in the case of graphs generated by three polynomials, we relate the distribution of leaves to the Sato-Tate distribution of Frobenius traces of elliptic curves. We also present extensive numerical results which we hope may shed some light on the distribution of leaves for larger families of polynomials.

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二次多项式族的泛函图

我们研究了由几个二次多项式生成的函数图，它们同时作用于具有奇特征的有限域上。我们得到了关于这类图中叶数的几个结果。特别地，在由三个多项式生成的图的情况下，我们将叶的分布与椭圆曲线的Frobenius迹的Sato-Tate分布联系起来。我们还给出了大量的数值结果，我们希望这些结果可以为更大多项式族的叶分布提供一些线索。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.