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papers

Publications (10)

math.DS2022

New Normal Forms For Degree Three Polynomials and Rational Functions

Heidi Benham, Alexander Galarraga, Benjamin Hutz +3

When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate que…

math.NT2020

A Unique Chief Series in the arboreal Galois Group of Belyi Maps

Wayne Peng

We give a complete description of the normal subgroups of arboreal Galois groups of Belyi maps. The normal groups form a unique chief series. We also carefully compute the discrimi…

math.NT2015

Wall's Conjecture and the ABC Conjecutre

George Grell, Wayne Peng

We show that the $ab c$ conjecture of Masser-OesterlÃ©-Szpiro for number fields implies that there are infinitely many non-Fibonacci-Wieferich primes. We also provide a new heuristi…

math.NT2021

Permutation polynomials: iteration of shift and inversion maps over finite fields

Anna Chlopecki, Juliano Levier-Gomes, Wayne Peng +2

We show that all permutations in $S_{n}$ can be generated by affine unicritical polynomials. We use the $PGL$ group structure to compute the cycle structure of permuta…

math.NT2021

A Tits alternative for rational functions

Jason P. Bell, Keping Huang, Wayne Peng +1

We prove an analog of the Tits alternative for rational functions. In particular, we show that if $S$ is a finitely generated semigroup of rational functions over the complex numbe…

math.DS2020

Unlikely intersection problems for restricted lifts of p-th power

Wayne Peng

I define a morphism on $C_{p}$ called a lift of $p$ -th power if its natural restriction to the residue field of $C_{p}$ is a $p$ -th power of some morphism. This defin…

math.DS2022

Integrality and Thurston Rigidity for Bicritical PCF Polynomials

Heidi Benham, Alexander Galarraga, Benjamin Hutz +3

We give an algebraic proof of an important consequence of Thurston rigidity for bicritical PCF polynomials with periodic critical points under certain mild assumptions. The key res…

math.NT2026

Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields

Wayne Peng, Yen-Ju Chen

This paper investigates the dynamical properties of the Dickson polynomials $D_{n} (x, I^\pm)$ of the first kind over finite fields, with an emphasis on the periodicity and algebraic str…

math.NT2015

ABC Implies There are Infinitely Many non-Fibonacci-Wieferich Primes - An Application of ABC Conjecture over Number Fields

Wayne Peng

In this paper, we define $X$ -base Fibonacci-Wieferich prime which is a generalized Wieferich prime where $X$ is a finite set of algebraic numbers. We are going to show that there a…

math.NT2025

Overgroups of the arboreal representation of PCF polynomial

Wayne Peng

Consider a number field $K$ and a rational function $f$ of degree greater than 1 over $K$ . By taking preimages of $I^\pm \in K$ under successive iterates of $f$ , an infinite $d$ -ary tr…