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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- polynomials defined over -adic fields and number fields, under a mild reduction hypothesis that…
math.NT2025
Towards the -adic derived Hecke algebra for weight one forms
Robin Zhang
This note outlines an approach to defining -adic Shimura classes and -adic derived Hecke operators on the completed cohomology of modular curves from upcoming work by the aut…
math.NT2025
Positive integral points on acyclic cluster varieties
Robin Zhang
We determine the number of positive integral points on -dimensional affine varieties associated to arbitrary generalized Cartan matrices. An application to the theo…