20 citations · 65 across the 9 of their papers we have counts for
11 papers
Automorphisms of general modular curves
Valerio Dose, Guido Maria Lido, Pietro Mercuri
We prove that for a geometrically connected modular curve of prime level larger than , all automorphisms are modular, i.e., they arise from the moduli interpretation of…
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…
Monotonicity of Equilibria in Nonatomic Congestion Games
Roberto Cominetti, Valerio Dose, Marco Scarsini
This paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify…
Phase Transitions of the Price-of-Anarchy Function in Multi-Commodity Routing Games
Roberto Cominetti, Valerio Dose, Marco Scarsini
We consider the behavior of the price of anarchy and equilibrium flows in nonatomic multi-commodity routing games as a function of the traffic demand. We analyze their smoothness w…
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 , for odd , and in , for . These towe…
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 and certain subgroups of their normalizers. We prove that if $n…
The Price of Anarchy in Routing Games as a Function of the Demand
Roberto Cominetti, Valerio Dose, Marco Scarsini
The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for s…
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_{…
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 for a subgroup of $\GL_2(\mathbb Z…
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 of prime level . We prove that if all the automorphisms preserve the cusps. Furthermore,…
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 associated to a non-split Cartan subgroup of . This allows us to compute the automorphism g…