Matt Olechnowicz

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20242026

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math.NT2025

Distribution of preperiodic points in one-parameter families of rational maps

Matt Olechnowicz

Let $f_{t}$ be a one-parameter family of rational maps defined over a number field $K$ . We show that for all $t$ outside of a set of natural density zero, every $K$ -rational preperio…

math.NT2024

Heights and morphisms in number fields

Matt Olechnowicz

We give a formula with explicit error term for the number of $K$ -rational points $P$ satisfying $H (f (P)) \leq X$ as $X \to \infty$ , where $f$ is a nonconstant morphism between proje…