3 papers
math.NT2026
Point counts, automorphisms, and gonalities of Shimura curves
Pietro Mercuri, Oana Padurariu, Frederick Saia +1
We implement an algorithm to compute the number of points over finite fields for the Shimura curves over and their Atkin--Lehner quotients. Our computations…
math.NT2025
Effective surjectivity of Galois representations of products of elliptic curves over function fields
Alina Cojocaru, Frederick Saia
We prove an effective surjectivity result for Galois representations of products of non-isotrivial, non-isogenous elliptic curves over certain function fields of characteristic …
math.NT2025
Shimura curve Atkin--Lehner quotients of genus at most two
Oana Padurariu, Frederick Saia
We provide a complete enumeration of all quotients of genus and of the Shimura curves over by non-trivial subgroups of Atkin--Lehner involutions.…