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

[1] A case of the dynamical Mordell-Lang conjecture [J].

Benedetto, Robert L. ;

Ghioca, Dragos ;

Kurlberg, Par ;

Tucker, Thomas J. .

MATHEMATISCHE ANNALEN, 2012, 352 (01) :1-26

[2]

Berczes A., INTERN MATH RES NOTI

[3] Powers in Orbits of Rational Functions: Cases of an Arithmetic Dynamical Mordell-Lang Conjecture [J].

Cahn, Jordan ;

Jones, Rafe ;

Spear, Jacob .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2019, 71 (04) :773-817

[4]

Chang MC, 2014, P AM MATH SOC, V142, P85

[5] Polynomial iteration in characteristic p [J].

Chang, Mei-Chu .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (11) :3412-3421

[6] AVOIDING ALGEBRAIC INTEGERS OF BOUNDED HOUSE IN ORBITS OF RATIONAL FUNCTIONS OVER CYCLOTOMIC CLOSURES [J].

Chen, Evan .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (10) :4189-4198

[7] On the concentration of points of polynomial maps and applications [J].

Cilleruelo, Javier ;

Garaev, Moubariz Z. ;

Ostafe, Alina ;

Shparlinski, Igor E. .

MATHEMATISCHE ZEITSCHRIFT, 2012, 272 (3-4) :825-837

[8] Cyclotomic diophantine problems (hilbert irreducibility and invariant sets for polynomial maps) [J].

Dvornicich, R. ;

Zannier, U. .

DUKE MATHEMATICAL JOURNAL, 2007, 139 (03) :527-554

[9] Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture [J].

Ghioca, Dragos ;

Tucker, Thomas J. ;

Zieve, Michael E. .

INVENTIONES MATHEMATICAE, 2008, 171 (02) :463-483

[10] LINEAR RELATIONS BETWEEN POLYNOMIAL ORBITS [J].

Ghioca, Dragos ;

Tucker, Thomas J. ;

Zieve, Michael E. .

DUKE MATHEMATICAL JOURNAL, 2012, 161 (07) :1379-1410

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