Fonction génératrice et congruences (application aux nombres de Bernoulli)
Fonctions digitales le long des nombres premiers
In a recent work we gave some estimations for exponential sums of the form , where Λ denotes the von Mangoldt function, f a digital function, and β a real parameter. The aim of this work is to show how these results can be used to study the statistical properties of digital functions along prime numbers.
Fonctions Entières Prenant des Valeurs Presque Entières aux Points d'une Progression Géométrique.
Fonctions multiplicatives et équations différentielles
Forcing sequences of positive integers
Formulas for sums of powers of integers by functional equations.
Formule exprimant les nombres de Cotes à l'aide des nombres de Stirling
Formules sommatoires et systèmes de numération liés aux substitutions
Fourier expansions and integral representations for Genocchi polynomials.
Fractions de Bernoulli-Carlitz et opérateurs -Zeta
On introduit une déformation des séries de Dirichlet d’une variable complexe , sous la forme d’un opérateur pour chaque nombre complexe , agissant sur les séries formelles sans terme constant en une variable . On montre que les fractions de Bernoulli-Carlitz sont les images de certains polynômes en par les opérateurs associés à la fonction de Riemann aux entiers négatifs.
Fraenkel's partition and Brown's decomposition.
Frequencies of factors in Arnoux-Rauzy sequences
Frontière du fractal de Rauzy et système de numération complexe
Full subsets of .
Fully degenerate poly-Bernoulli numbers and polynomials
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
Function minimum associated to a congruence on integral n-tuple space.
Functions of slow increase and integer sequences.
Functorial concepts of complexity for finite automata.
Funzione generatrice e polinomi incompleti di Fibonacci e Lucas
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.
Further remarks on Diophantine quintuples
A set of m positive integers with the property that the product of any two of them is the predecessor of a perfect square is called a Diophantine m-tuple. Much work has been done attempting to prove that there exist no Diophantine quintuples. In this paper we give stringent conditions that should be met by a putative Diophantine quintuple. Among others, we show that any Diophantine quintuple a,b,c,d,e with a < b < c < d < ed < 1.55·1072b < 6.21·1035c = a + b + 2√(ab+1) and ...