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math.NT2025
A characteristic p analogue of the André--Pink--Zannier conjecture
Yeuk Hay Joshua Lam, Ananth N. Shankar
We investigate the analogue of the André--Pink--Zannier conjecture in characteristic . Precisely, we prove it for ordinary function field-valued points with big monodromy, in Sh…
math.NT2025
On Siegel's problem and Dwork's conjecture for -functions
Javier Fresán, Yeuk Hay Joshua Lam, Yichen Qin
We answer in the negative Siegel's problem for -functions, as formulated by Fischler and Rivoal. Roughly, we prove that there are -functions that cannot be written as polynom…
math.AG2025
Algebraicity and integrality of solutions to differential equations
Yeuk Hay Joshua Lam, Daniel Litt
We formulate a conjecture classifying algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the primes appearing in the denominators of the coe…