4 papers
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…
A survey about Hidden Subgroup Problem from a mathematical and cryptographic perspective
Simone Dutto, Pietro Mercuri, Nadir Murru +1
We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, wher…
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…