4 citations · 10 across the 12 of their papers we have counts for
13 papers
A one parameter family of Volterra-type operators
Francesco Battistoni, Giuseppe Molteni
For every and let be the operator defined via the equality . We study the…
The first and second moment for the length of the period of the continued fraction expansion for
Francesco Battistoni, Loïc Grenié, Giuseppe Molteni
Let be any positive and non square integer. We prove an upper bound for the first two moments of the length of the period of the continued fraction expansion for $\sqrt{…
Generalized Pohst inequality and small regulators
Francesco Battistoni, Giuseppe Molteni
Current methods for the classification of number fields with small regulator depend mainly on an upper bound for the discriminant, which can be improved by looking for the best pos…
On the trace of the integers of a number field
Francesco Battistoni, Toufik Zaïmi
Let denote the trace -module homomorphism defined on the ring of the integers of a number field We show that $Tr(\mathcal{O}_{L})\varsubset…
Ranks of elliptic curves over of small degree in
Francesco Battistoni, Sandro Bettin, Christophe Delaunay
We study elliptic surfaces over with coefficients of a Weierstrass model being polynomials in with degree at most 2. We derive an explicit expressio…
On the typical rank of elliptic curves over
Francesco Battistoni, Sandro Bettin, Christophe Delaunay
We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This conf…
Arithmetic equivalence for non-geometric extensions of global function fields
Francesco Battistoni, Hassan Oukhaba
In this paper we study couples of finite separable extensions of the function field which are arithmetically equivalent, i.e. such that prime ideals of $\mathbb{F…
An elementary proof for a generalization of a Pohst's inequality
Francesco Battistoni, Giuseppe Molteni
Let and where the supremum is taken over the $n…
A conjectural improvement for inequalities related to regulators of number fields
Francesco Battistoni
An inequality proved firstly by Remak and then generalized by Friedman shows that there are only finitely many number fields with a fixed signature and whose regulator is less than…
Discriminants of number fields and surjectivty of trace homomorphism on rings of integers
Francesco Battistoni
In this note we give a brief survey of the most elementary criteria used to determine the surjectivity of the trace operator on the ring of integers of a number field . Furtherm…
On small discriminants of number fields of degree 8 and 9
Francesco Battistoni
We classify all the number fields with signature (4,2), (6,1), (1,4) and (3,3) having discriminant lower than a specific upper bound. This completes the search for minimum discrimi…
On Locally GCD Equivalent Number Fields
Francesco Battistoni
Local GCD Equivalence is a relation between extensions of number fields which is weaker than the classical arithmetic equivalence. It was originally studied by Lochter with Weak Kr…
The minimum discriminant of number fields of degree 8 and signature (2,3)
Francesco Battistoni
In this paper we describe how to use the algorithmic methods provided by Hunter and Pohst in order to give a complete classification of number fields of degree 8 and signature (2,3…