Erik Holmes

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math.NT2023

Adelic perturbation of rational functions and applications

Félix Baril Boudreau, Erik Holmes, Khoa D. Nguyen

Let $\sum a_{n} x^{n} \in Q ˉ [[x]]$ be the power series representation of a rational function and let $f : {0, 1, \dots} \to Q ˉ$ be a so-called almost q…

math.NT2022

On the shapes of pure prime degree number fields

Erik Holmes

For $p$ prime and $ℓ = \frac{p - 1}{2}$ , we show that the shapes of pure prime degree number fields lie on one of two $ℓ$ -dimensional subspaces of the space of shapes, and whic…