Effective asymptotic for some nonlinear recurrences and almost doubly-exponential sequences.
Effective bounds for the zeros of linear recurrences in function fields
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 , where is a linear recurring sequence of polynomials and is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].
Effective solution of the D(-1)-quadruple conjecture
Eine Bemerkung zur Periodenlängenbestimmung bei einem verallgemeinerten Fibonacci-Generator.
Embedding the conjecture in a context.
Endomorphismes d’algèbres de suites
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 dans .
Equations in one variable over function fields
Equations in the Hadamard ring of rational functions
Let be a number field. It is well known that the set of recurrencesequences with entries in 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 is a recurrence sequence and suppose that all the have a root in the field ; then (after...
Equidistribution of linear recurring sequences in finite fields, II
Euler indicators of binary recurrence sequences.
Eulerian numbers with fractional order parameters.
Extension d'un théorème de Pólya-Cantor à des séries rationnelles en variables non commutatives