4 papers · 1 filter
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…
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…
Greenberg's conjecture for real quadratic number fields
Pietro Mercuri, Maurizio Paoluzi, René Schoof
We compute the -class groups of the fields in the cyclotomic -extensions of the real quadratic fields of discriminant . In all cases the ord…
Modular forms invariant under non-split Cartan subgroups
Pietro Mercuri, Rene Schoof
In this paper we describe a method for computing a basis for the space of weight cusp forms invariant under a non-split Cartan subgroup of prime level . As an application we…