V. Dose

activity

20142026

most citedThe Price of Anarchy in Routing Games as a Function of the Demand

20 citations · 65 across the 9 of their papers we have counts for

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8 papers · 1 filter

math.NT2026

Automorphisms of general modular curves

Valerio Dose, Guido Maria Lido, Pietro Mercuri

We prove that for a geometrically connected modular curve $X_{H}$ of prime level larger than $311$ , all automorphisms are modular, i.e., they arise from the moduli interpretation of…

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.NT2020★ 6 cited

Automorphisms of Cartan modular curves of prime and composite level

Valerio Dose, Guido Lido, Pietro Mercuri

We study the automorphisms of modular curves associated to Cartan subgroups of $GL_{2} (Z / n Z)$ and certain subgroups of their normalizers. We prove that if $n…

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.NT2015★ 6 cited

On the automorphisms of the non-split Cartan modular curves of prime level

Valerio Dose

We study the automorphisms of the non-split Cartan modular curves $X_{n s} (p)$ of prime level $p$ . We prove that if $p \geq 37$ all the automorphisms preserve the cusps. Furthermore,…

math.NT2014★ 13 cited

The automorphism group of the non-split Cartan modular curve of level 11

Valerio Dose, Julio Fernández, Josep González +1

We derive equations for the modular curve $X_{n s} (11)$ associated to a non-split Cartan subgroup of $GL_{2} (F_{11})$ . This allows us to compute the automorphism g…