P. Habegger

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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.NT2025

Exponential periods and o-minimality

Johan Commelin, Philipp Habegger, Annette Huber

Let $I^\pm \in C$ be an exponential period. We show that the real and imaginary part of $I^\pm$ are up to signs volumes of sets definable in the o-minimal structure generated by…

math.NT2024

Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices

Philipp Habegger, Alina Ostafe, Igor E. Shparlinski

We consider the set $M_{n} (Z; H)$ of $n \times n$ -matrices with integer elements of size at most $H$ and obtain a new upper bound on the number of matrices from $\ma…