Robin Zhang

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math.NT2025

Uniform bounds on periodic points of polynomials with good reduction

Isaac Rajagopal, Robin Zhang

We establish effective bounds on the number of periodic points of degree- $d$ polynomials $ϕ$ defined over $p$ -adic fields and number fields, under a mild reduction hypothesis that…

math.NT2025

Towards the $p$ -adic derived Hecke algebra for weight one forms

Robin Zhang

This note outlines an approach to defining $p$ -adic Shimura classes and $p$ -adic derived Hecke operators on the completed cohomology of modular curves from upcoming work by the aut…

math.NT2025

A positive Siegel theorem: Dynkin friezes and positive Mordell-Schinzel

Robin Zhang

We determine the number of positive integral points on $n$ -dimensional affine varieties associated to arbitrary $n \times n$ generalized Cartan matrices. An application to the theo…

Uniform bounds on periodic points of polynomials with good reduction

Towards the p-adic derived Hecke algebra for weight one forms

A positive Siegel theorem: Dynkin friezes and positive Mordell-Schinzel

Towards the $p$ -adic derived Hecke algebra for weight one forms