Claudio Stirpe

activity

20122025

most citedDouble Covers of Cartan Modular Curves

4 citations · 10 across the 6 of their papers we have counts for

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8 papers · 1 filter

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★ 4 cited

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★ 3 cited

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…

math.NT2014

Classification of Algebraic Function Fields with Class Number One

Pietro Mercuri, Claudio Stirpe

In this paper we prove that there are exactly eight function fields, up to isomorphism, over finite fields with class number one.

math.NT2013

A counterexample to 'Algebraic function fields with small class number'

Claudio Stirpe

I give a counter example of function field over GF(2) of genus 4 with class number one. This result contradicts a previous result in [2], Section 2 so that proof is wrong.

math.NT2012★ 1 cited

An upper bound for the genus of a curve without points of small degree

Claudio Stirpe

In this paper I prove that for any prime $p$ there is a constant $C_{p} > 0$ such that for any $n > 0$ and for any $p$ -power $q$ there is a smooth, projective, absolutely irreducible cur…