Rufei Ren

activity

20162026

most citedSlopes for higher rank Artin-Schreier-Witt Towers

17 citations · 23 across the 11 of their papers we have counts for

collaborators

11 papers

math.NT2026

Coefficient-Level Böttcher Theory for Wild Superattracting Germs of Degree $p^{e}$

Rufei Ren

Let $p$ be an odd prime, let $e \geq 2$ , and put $q = p^{e}$ . We study the wild family \[ φ_{r,e}(x)=x^q+qp^r x^{q+1}=x^{p^e}+p^{r+e}x^{p^e+1} \qquad (r\ge0), \] and the inverse Böttcher…

math.NT2022

The slope-invariant of local ghost series under direct sum

Rufei Ren

The ghost conjecture is first provided by Bergdall and Pollack in [BP-1,BP-2] to study the Up-slopes of spaces of modular forms, which, so far, has already brought plenty of import…

math.NT2022

Localized Gouvêa-Mazur conjecture

Rufei Ren

Gouvêa-Mazur [GM] made a conjecture on the local constancy of slopes of modular forms when the weight varies $p$ -adically. Since one may decompose the space of modular forms accord…

math.NT2020★ 2 cited

Spectral halo for Hilbert modular forms

Rufei Ren, Bin Zhao

Let $F$ be a totally real field and $p$ be an odd prime which splits completely in $F$ . We prove that the eigenvariety associated to a definite quaternion algebra over $F$ satisfie…

math.DS2020

Non-Linearizability of power series over complete non-Archimedean fields of positive characteristic

Rufei Ren

In [H-Y83], Herman and Yoccoz prove that for any given locally analytic (at $z = 0$ ) power series $f (z) = z (λ + \sum_{i = 1}^{\infty} a_{i} z^{i})$ over a complete non-Archimedean field of charac…

math.DS2019

Primitive prime divisors in the critical orbits of one-parameter families of rational polynomials

Rufei Ren

For a rational polynomial $f$ and rational numbers $c, u$ , we put $f_{c} (x) := f (x) + c$ , and consider the Zsigmondy set $Z (f_{c}, u)$ associated to the sequence $\{f_c^n(u)-u\}_{…

math.NT2018★ 1 cited

Iteration of Polynomials $A X^{d} + C$ Over Finite Fields

Rufei Ren

For a polynomial $f (X) = A X^{d} + C \in F_{p} [X]$ with $A \neq = 0$ and $d \geq 2$ , we prove that if $d ∣ p - 1$ and $f^{i} (0) \neq = f^{j} (0)$ for $0 \leq i < j \leq N$ , then $\#f^N(\mathbb{F}_…

math.NT2017★ 3 cited

Generic Newton polygon for exponential sums in $n$ variables with parallelotope base

Rufei Ren

Let $p$ be a prime number. Every $n$ -variable polynomial $f (x)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of varieties whose Galoi…

math.NT2017

Newton slopes for twisted Artin--Schreier--Witt Towers

Rufei Ren

We fix a monic polynomial $f (x) \in F_{q} [x]$ over a finite field of characteristic $p$ of degree relatively prime to $p$ . Let $a \mapsto ω (a)$ be the Teichmüller lift of $\ma…

math.NT2017

Generic Newton polygon for exponential sums in two variables with triangular base

Rufei Ren

Let $p$ be a prime number. Every two-variable polynomial $f (x_{1}, x_{2})$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of surfaces whose Galois gro…

math.NT2016★ 17 cited

Slopes for higher rank Artin-Schreier-Witt Towers

Rufei Ren, Daqing Wan, Liang Xiao +1

We fix a monic polynomial $f ˉ (x) \in F_{q} [x]$ over a finite field of characteristic $p$ , and consider the $Z_{p^{ℓ}}$ -Artin-Schreier-Witt tower defined by $…

Coefficient-Level Böttcher Theory for Wild Superattracting Germs of Degree pe

The slope-invariant of local ghost series under direct sum

Localized Gouvêa-Mazur conjecture

Spectral halo for Hilbert modular forms

Non-Linearizability of power series over complete non-Archimedean fields of positive characteristic

Primitive prime divisors in the critical orbits of one-parameter families of rational polynomials

Iteration of Polynomials AXd+C Over Finite Fields

Generic Newton polygon for exponential sums in n variables with parallelotope base

Newton slopes for twisted Artin--Schreier--Witt Towers

Generic Newton polygon for exponential sums in two variables with triangular base

Slopes for higher rank Artin-Schreier-Witt Towers

Coefficient-Level Böttcher Theory for Wild Superattracting Germs of Degree $p^{e}$

Iteration of Polynomials $A X^{d} + C$ Over Finite Fields

Generic Newton polygon for exponential sums in $n$ variables with parallelotope base