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math.NT2026
Dynamical Canonical Heights and Finite Trees
Philipp Habegger, Harry Schmidt
We establish lower bounds for the canonical height of a wandering point that decays like the square of the field degree. Our methods and results apply to centered, postcritically f…
math.NT2026
Uniform sum-product phenomenon for algebraic groups and Bremner's conjecture
Joseph Harrison, Akshat Mudgal, Harry Schmidt
In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this…