F. Saia

activity

20162025

most citedCM points on Shimura curves via QM-equivariant isogeny volcanoes

1 citations · 1 across the 4 of their papers we have counts for

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6 papers · 1 filter

math.NT2025

Replacement dynamics of binary quadratic forms

Raghav Bhutani, Frederick Saia

For an $S$ -valued function $f$ of $m \geq 1$ variables we consider the dynamical process in which the output $f (v)$ replaces exactly one entry of the input $\overline{v}…

math.NT2025

Counting points on some genus zero Shimura curves

Tyler Genao, Tristan Phillips, Fredderick Saia +2

We count certain abelian surfaces with potential quaternionic multiplication defined over a number field $K$ by counting points of bounded height on some genus zero Shimura curves.

math.NT2024

Bielliptic Shimura curves $X_{0}^{D} (N)$ with nontrivial level

Oana Padurariu, Frederick Saia

We work towards completely classifying all bielliptic Shimura curves $X_{0}^{D} (N)$ with nontrivial level $N$ coprime to $D$ , extending a result of Rotger that provided such a classifi…

math.NT2022

CM Elliptic Curves: Volcanoes, Reality and Applications, Part II

Pete L. Clark, Frederick Saia

Let $M ∣ N$ be positive integers, and let $Δ$ be the discriminant of an order in an imaginary quadratic field $K$ . When $Δ_{K} < - 4$ , the first author determined the fiber of the…

math.NT2022★ 1 cited

CM points on Shimura curves via QM-equivariant isogeny volcanoes

Frederick Saia

We study CM points on the Shimura curves $X_{0}^{D} (N)_{/ Q}$ and $X_{1}^{D} (N)_{/ Q}$ , parametrizing abelian surfaces with quaternionic multiplication and extra level stru…

math.NT2016

Classically Integral Quadratic Forms Excepting at Most Two Values

Madeleine Barowsky, William Damron, Andres Mejia +3

Let $S \subseteq N$ be finite. Is there a positive definite quadratic form that fails to represent only those elements in $S$ ? For $S = \emptyset$ , this was solved (for cl…