Claudio Stirpe

activity

20162025

most citedHigh Order Elements in Finite Fields Arising from Recursive Towers

2 citations · 2 across the 2 of their papers we have counts for

collaborators

5 papers

math.NT2025

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.NT2020★ 2 cited

High Order Elements in Finite Fields Arising from Recursive Towers

Valerio Dose, Pietro Mercuri, Ankan Pal +1

We provide a recipe to construct towers of fields producing high order elements in $GF (q, 2^{n})$ , for odd $q$ , and in $GF (2, 2 \cdot 3^{n})$ , for $n \geq 1$ . These towe…

math.NT2017

Double Covers of Cartan Modular Curves

Valerio Dose, Pietro Mercuri, Claudio Stirpe

We present a strategy to obtain explicit equations for the modular double covers associated respectively to both a split and a non-split Cartan subgroup of $\text{GL}_2(\mathbb F_{…

math.NT2016

Modular Curves with many Points over Finite Fields

Valerio Dose, Guido Lido, Pietro Mercuri +1

We describe an algorithm to compute the number of points over finite fields on a broad class of modular curves: we consider quotients $X_{H} / W$ for $H$ a subgroup of $\GL_2(\mathbb Z…