UNLIKELY INTERSECTIONS OVER FINITE FIELDS: POLYNOMIAL ORBITS IN SMALL SUBGROUPS

被引：0

作者：

Merai, Laszlo ^{[1
]}

Shparlinski, Igor E. ^{[2
]}

机构：

[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, Altenberger Str 69, A-4040 Linz, Austria

[2] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 02期

基金：

奥地利科学基金会; 澳大利亚研究理事会;

关键词：

Polynomial iterations; polynomials semigroups; multiplicative subgroup; finite fields; unlikely intersection; MORDELL-LANG CONJECTURE; RATIONAL FUNCTIONS; MAPS; SUMS;

D O I：

10.3934/dcds.2020070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We estimate the frequency of polynomial iterations which fall in a given multiplicative subgroup of a finite field of p elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first N elements in an orbit. We derive these from more general results about sequences of compositions on a fixed set of polynomials.

引用

页码：1065 / 1073

页数：9

共 28 条

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