2 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
Maximal curves over finite fields and a modular isogeny
Valerio Dose, Guido Lido, Pietro Mercuri +1
We prove the existence of curves of genus and over the field with elements, reaching the Hasse-Weil-Serre upper bound. These curves are quotients of modular curves…