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Effective bounds for the zeros of linear recurrences in function fields

Clemens Fuchs, Attila Pethő (2005)

Journal de Théorie des Nombres de Bordeaux

In this paper, we use the generalisation of Mason’s inequality due to Brownawell and Masser (cf. [8]) to prove effective upper bounds for the zeros of a linear recurring sequence defined over a field of functions in one variable.Moreover, we study similar problems in this context as the equation G n ( x ) = G m ( P ( x ) ) , ( m , n ) ∈ ℕ 2 , where ( G n ( x ) ) is a linear recurring sequence of polynomials and P ( x ) is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].

Endomorphismes d’algèbres de suites

Ahmed Ait-Mokhtar, Abdelkader Necer, Alain Salinier (2008)

Journal de Théorie des Nombres de Bordeaux

Cet article traite des endomorphismes de l’algèbre de Hadamard des suites et plus particulièrement de l’algèbre des suites récurrentes linéaires. Il caractérise les endomorphismes continus de l’algèbre des suites et contient, dans le cas d’un corps commutatif de caractéristique nulle, une détermination complète des endomorphismes continus de l’algèbre des suites récurrentes linéaires grâce à la notion nouvelle d’application semi-affine de ℕ dans ℕ .

Equations in the Hadamard ring of rational functions

Andrea Ferretti, Umberto Zannier (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let K be a number field. It is well known that the set of recurrencesequences with entries in K is closed under component-wise operations, and so it can be equipped with a ring structure. We try to understand the structure of this ring, in particular to understand which algebraic equations have a solution in the ring. For the case of cyclic equations a conjecture due to Pisot states the following: assume { a n } is a recurrence sequence and suppose that all the a n have a d th root in the field K ; then (after...

Funzione generatrice e polinomi incompleti di Fibonacci e Lucas

Wenchang Chu, Valentina Vicenti (2003)

Bollettino dell'Unione Matematica Italiana

I numeri incompleti di Fibonacci e di Lucas, introdotti da Filipponi (1996), sono entrambi generalizzati in forma di polinomi. Le loro funzioni generatrici ridondanti, naturali e condizionate sono stabilite attraverso serie formali di potenze. Le funzioni generatrici relative alle sequenze di numeri dovute a Pinter e Srivastava (1999) sono contenute come casi particolari.

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