This page contains a regularly-updated list of my published works, as well as works currently under review. For search friendliness, I’ve included brief abstracts and links to the arXiv, where applicable.

*Arithmetic** Pro**perties** of Picard-Fuchs Equations and Holonomic Recurrences:*

The coefficient series of the holomorphic Picard-Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties, whice have been widely studied for torsion-free, genus zero congruence subgroups of index 6 and 12 (e.g. the Beauville families). Here, we consider the Picard-Fuchs solutions associated to general elliptic families, with a particular focus on the index 24 congruence subgroups.

We prove that elliptic families over admit linear reparametrizations such that their associated Picard-Fuchs solutions lie in . A sufficient condition is given such that the same holds for holomorphic solutions at infinity. An Atkin-Swinnerton-Dyer congruence is proven for the coefficient series attached to . We conclude with a consideration of asymptotics, wherein we prove that many coefficient series satisfy asymptotic expressions of the form . Certain arithmetic results extend to the study of general holonomic recurrences.

(Joint work with Zane Kun Li, to appear in the *Journal of Number Theory.*)

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