P. Mercuri

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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 $X_{0}^{D} (N)$ over $Q$ 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 $7$ and $12$ over the field with $1 1^{5}$ elements, reaching the Hasse-Weil-Serre upper bound. These curves are quotients of modular curves…

math.NT2025

Greenberg's conjecture for real quadratic number fields

We compute the $3$ -class groups $A_{n}$ of the fields $F_{n}$ in the cyclotomic $Z_{3}$ -extensions of the real quadratic fields of discriminant $f < 100, 000$ . In all cases the ord…