F. Saia

activity

20242026

collaborators

4 papers

math.NT2026

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

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.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

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…

Replacement dynamics of binary quadratic forms

Bielliptic Shimura curves X0D​(N) with nontrivial level

Counting points on some genus zero Shimura curves

CM points on Shimura curves via QM-equivariant isogeny volcanoes

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