Rufei Ren

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20182020

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math.NT2020

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.NT2018

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}_…

Spectral halo for Hilbert modular forms

Iteration of Polynomials AXd+C Over Finite Fields

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