5 citations · 9 across the 11 of their papers we have counts for
12 papers
Gaps in binary cyclotomic polynomials
Antonio Cafure, Eda Cesaratto
For odd prime numbers , let be the binary cyclotomic polynomial of order . In this paper, we prove that the second gap of is the maxi…
Shannon Weights for binary dynamical recurrent sources of zero entropy
Ali Akhavi, Eda Cesaratto, Frédéric Paccaut +2
A probabilistic source is defined as the set of infinite words (over a given denumerable alphabet) endowed with a probability . The paper deals with general binary sources where…
Poisson genericity in numeration systems with exponentially mixing probabilities
Nicolás Álvarez, Verónica Becher, Eda Cesaratto +3
We define Poisson genericity for infinite sequences in any finite or countable alphabet with an invariant exponentially-mixing probability measure. A sequence is Poisson generic if…
Lochs-type theorems beyond positive entropy
Valérie Berthé, Eda Cesaratto, Pablo Rotondo +1
Lochs' theorem and its generalizations are conversion theorems that relate the number of digits determined in one expansion of a real number as a function of the number of digits g…
Binary Cyclotomic Polynomials: Representation via Words and Algorithms
Antonio Cafure, Eda Cesaratto
Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the bina…
On the number of words with restrictions on the number of symbols
Verónica Becher, Eda Cesaratto
We show that, in an alphabet of symbols, the number of words of length whose number of different symbols is away from , which is the value expected by the Poisson…
Gaussian Behavior of Quadratic Irrationals
Eda Cesaratto, Brigitte Vallée
We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit…
The distribution of factorization patterns on linear families of polynomials over a finite field
Eda Cesaratto, Guillermo Matera, Mariana Pérez
We obtain estimates on the number of elements on a linear family of monic polynomials of of degree having factori…
The number of reducible space curves over a finite field
Eda Cesaratto, Joachim von zur Gathen, Guillermo Matera
"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. Th…
On the value set of small families of polynomials over a finite field, I
Eda Cesaratto, Guillermo Matera, Mariana Pérez +1
We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},..., a_{d-s}…
Multifractal Spectrum and Thermodynamical Formalism of the Farey Tree
M. Piacquadio Losada, E. Cesaratto
The task of comparing the Hausdorff spectrum, the computational spectrum, and the Legendre spectrum of a fractal set endowed with a probability measure, was tackled by several auth…
On the Hausdorff dimension of certain sets arising in Number Theory
Eda Cesaratto
This paper has been withdrawn Any real number in the unit interval can be expressed as a continued fraction . Subsets of zero measure are obtained by im…