Ge Zhang

activity

20212026

most citedSpace spanned by characteristic exponents

1 citations · 2 across the 9 of their papers we have counts for

collaborators

10 papers

math.NT2026

A Bogomolov property for moduli spaces of polynomials over abelian extensions

Geng-Rui Zhang

Let $d \geq 2$ be an integer, and let $MPoly^{d}$ be the moduli space of degree- $d$ polynomials. For every number field $K$ , we prove that there exists $ε_{K, d} > 0$ such…

math.DS2026

Generic reconstruction of rational maps from multipliers of periods one and two

Geng-Rui Zhang

For every integer $d \geq 2$ and every field of characteristic different from $2$ , we prove that on the moduli space $M_{d}$ of degree- $d$ rational maps, the multiplier spect…

math.NT2026

$13$ unknowns over quadratic integer rings and Lucas congruences

Geng-Rui Zhang

For every quadratic number field $K$ , we prove a uniform $3$ -unknown Diophantine definition of integer tuples in $O_{K}$ , allowing finitely many polynomial nonvanishing con…

math.DS2026

Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type

Geng-Rui Zhang

Let $f, g \in C [z] ∖ C$ and $c \in C [z]$ . Suppose that $deg (c) = 1$ if $deg (f) = deg (g) = 1$ . Using the theory of Presburger arithm…

math.DS2026

Rigidity of Lyapunov exponents for polynomials

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

Let $f, g \in Q [z]$ be polynomials of degree $d \geq 2$ with disconnected Julia sets. We prove that they have the same Lyapunov exponent $\mathcal{L}_f=\mathcal{L}_g…

math.DS2025

Cyclotomic integral points for affine dynamics

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

Let $f : A^{N} \to A^{N}$ be a regular endomorphism of algebraic degree $d \geq 2$ (i.e., $f$ extends to an endomorphism on $P^{N}$ of algebraic degree $d$ ) defined…

math.DS2025

On the multiplier spectrum of polynomials

Geng-Rui Zhang

We prove several results on the multiplier spectrum of polynomials. We provide a detailed proof of the theorem stating that the multiplier spectrum morphism is generically injectiv…

math.DS2023★ 1 cited

Space spanned by characteristic exponents

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

We prove several rigidity results on multiplier spectrum and length spectrum. For example, we show that for every non-exceptional rational map $f:\mathbb{P}^1(\mathbb{C})\to\mathbb…

math.NT2023

Realizability of Some Combinatorial Sequences

Geng-Rui Zhang

A sequence $a = (a_{n})_{n = 1}^{\infty}$ of non-negative integers is called realizable if there is a self-map $T : X \to X$ on a set $X$ such that $a_{n}$ is equal to the number of periodic po…

math.NT2021★ 1 cited

$Q ∖ Z$ is diophantine over $Q$ with 32 unknowns

Geng-Rui Zhang, Zhi-Wei Sun

In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that $Q ∖ Z$ is diophantine over $Q$ , i.e., there is a polynomial $P(t,x…

A Bogomolov property for moduli spaces of polynomials over abelian extensions

Generic reconstruction of rational maps from multipliers of periods one and two

13 unknowns over quadratic integer rings and Lucas congruences

Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type

Rigidity of Lyapunov exponents for polynomials

Cyclotomic integral points for affine dynamics

On the multiplier spectrum of polynomials

Space spanned by characteristic exponents

Realizability of Some Combinatorial Sequences

Q∖Z is diophantine over Q with 32 unknowns

$13$ unknowns over quadratic integer rings and Lucas congruences

$Q ∖ Z$ is diophantine over $Q$ with 32 unknowns