9 citations · 50 across the 23 of their papers we have counts for
23 papers · 1 filter
Algebraic integers with continued fraction expansions containing palindromes and square roots with prescribed periods
Stefano Barbero, Umberto Cerruti, Nadir Murru +1
We present a characterization of the algebraic integers with continued fraction expansions of the form , where is a pali…
An isomorphism between the convolution product and the componentwise sum connected to the D'Arcais numbers and the Ramanujan tau function
Stefano Barbero, Umberto Cerruti, Nadir Murru
Given a commutative ring with identity, let be the set of sequences of elements in . We investigate a novel isomorphism between and , where…
Approximations of algebraic irrationalities with matrices
Stefano Barbero, Umberto Cerruti, Nadir Murru
We discuss the use of matrices for providing sequences of rationals that approximate algebraic irrationalities. In particular, we study the regular representation of algebraic exte…
Linear fractional transformations and non-linear leaping convergents of some continued fractions
Christopher Havens, Stefano Barbero, Umberto Cerruti +1
For an infinite continued fraction and a linear fractional transformation, we study the continued fraction expansion of and its c…
On the operations of sequences in rings and binomial type sequences
Stefano Barbero, Umberto Cerruti, Nadir Murru
Given a commutative ring with identity , many different and interesting operations can be defined over the set of sequences of elements in . These operations can also g…
Groups and monoids of Pythagorean triples connected to conics
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer t…
Some combinatorial properties of the Hurwitz series ring
Stefano Barbero, Umberto Cerruti, Nadir Murru
We study some properties and perspectives of the Hurwitz series ring , for a commutative ring with identity . Specifically, we provide a closed form for the invertible…
Linear divisibility sequences and Salem numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We study linear divisibility sequences of order 4, providing a characterization by means of their characteristic polynomials and finding their factorization as a product of linear…
The Biharmonic mean
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic…
Polynomial sequences on quadratic curves
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper we generalize the study of Matiyasevich on integer points over conics, introducing the more general concept of radical points. With this generalization we are able to…
Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper, we study the representation of pi as sum of arcotangents. In particular, we obtain new identities by using linear recurrent sequences. Moreover, we provide a method…
Colored compositions, Invert operator and elegant compositions with the "black tie"
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an importan…
Construction and Composition of Rooted Trees via Descent Functions
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study…
Identities Involving Zeros of Ramanujan and Shanks Cubic Polynomials
Stefano Barbero, Umberto Cerruti, Nadir Murru +1
In this paper we highlight the connection between Ramanujan cubic polynomials (RCPs) and a class of polynomials, the Shanks cubic polynomials (SCPs), which generate cyclic cubic fi…
Periodic representations for cubic irrationalities
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper we present some results related to the problem of finding periodic representations for algebraic numbers. In particular, we analyze the problem for cubic irrationalit…
Squaring the magic squares of order 4
Stefano Barbero, Umberto Cerruti, Nadir Murru
In this paper, we present the problem of counting magic squares and we focus on the case of multiplicative magic squares of order 4. We give the exact number of normal multiplicati…
Accelerations of generalized Fibonacci sequences
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate s…
Fixed Sequences for a Generalization of the Binomial Interpolated Operator and for some Other Operators
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
This paper is devoted to the study of eigen-sequences for some important operators acting on sequences. Using functional equations involving generating functions, we completely sol…
A Generalization of the Binomial Interpolated Operator and its Action on Linear Recurrent Sequences
Stefano Barbero, Umberto Cerruti, Nadir Murru
In this paper we study the action of a generalization of the Binomial interpolated operator on the set of linear recurrent sequences. We find how the zeros of characteristic polyno…
Generalized Rédei rational functions and rational approximations over conics
Stefano Barbero, Umberto Cerruti, Nadir Murru
In this paper we study a general class of conics starting from a quotient field. We give a group structure over these conics generalizing the construction of a group over the Pell…
Transforming Recurrent Sequences by Using the Binomial and Invert Operators
Stefano Barbero, Umberto Cerruti, Nadir Murru
In this paper we study the action of the Binomial and Invert (interpolated) operators on the set of linear recurrent sequences. We prove that these operators preserve this set, and…
Solving the Pell equation via Rédei rational functions
Stefano Barbero, Umberto Cerruti, Nadir Murru
In this paper, we define a new product over , which allows us to obtain a group isomorphic to with the usual product. This operation unexpectedly…
Catalan Moments
Stefano Barbero, Umberto Cerruti
This paper is essentially devoted to the study of some interesting relations among the well known operators (the interpolated Invert), (the interpolated Binomia…