FUNCTIONAL GRAPHS OF FAMILIES OF QUADRATIC POLYNOMIALS

被引：1

作者：

Mans, Bernard ^{[1
]}

Sha, Min ^{[2
]}

Shparlinski, Igor E. ^{[3
]}

Sutantyo, Daniel ^{[1
]}

机构：

[1] Macquarie Univ, Sch Comp, Sydney, NSW 2109, Australia

[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

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

来源：

MATHEMATICS OF COMPUTATION | 2023年 / 92卷 / 343期

基金：

澳大利亚研究理事会;

关键词：

Finite field; functional graph; graph leaves; quadratic polynomial; elliptic curve; ELLIPTIC-CURVES; RATIONAL MAPS; ITERATION; MODULO; NUMBER; PERIODS; POINTS; FIELD;

D O I：

10.1090/mcom/3838

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study functional graphs generated by several quadratic poly-nomials, 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.

引用

页码：2307 / 2331

页数：25

共 50 条

[31] Tension polynomials of graphs
Kochol, M
JOURNAL OF GRAPH THEORY, 2002, 40 (03) : 137 - 146
[32] Chain polynomials of graphs
Read, RC
DISCRETE MATHEMATICS, 2003, 265 (1-3) : 213 - 235
[33] Acyclic polynomials of graphs
Barton, Caroline
Brown, Jason, I
Pike, David A.
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2022, 82 : 146 - 181
[34] PERMANENTAL POLYNOMIALS OF GRAPHS
MERRIS, R
REBMAN, KR
WATKINS, W
LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 38 (JUN) : 273 - 288
[35] Families of polynomials and their specializations
Bodin, Arnaud
Debes, Pierre
Najib, Salah
JOURNAL OF NUMBER THEORY, 2017, 170 : 390 - 408
[36] Quadratic forms on graphs
Noga Alon
Konstantin Makarychev
Yury Makarychev
Assaf Naor
Inventiones mathematicae, 2006, 163 : 499 - 522
[37] QUADRATIC POLYNOMIALS AND HENON ATTRACTOR
YOCCOZ, JC
ASTERISQUE, 1991, (201) : 143 - 165
[38] IDEALS GENERATED BY QUADRATIC POLYNOMIALS
Ananyan, Tigran
Hochster, Melvin
MATHEMATICAL RESEARCH LETTERS, 2012, 19 (01) : 233 - 244
[39] Infinitely renormalizable quadratic polynomials
Jiang, YP
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (11) : 5077 - 5091
[40] Mating Siegel quadratic polynomials
Yampolsky, M
Zakeri, S
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 14 (01) : 25 - 78

← 1 2 3 4 5 →