Entire functions on nuclear sequence spaces.
Entrelacement de co-Poisson
On connaît le lien intime qui existe entre les équations fonctionnelles des fonctions et les formules sommatoires dont le prototype est donné par celle de Poisson. Ce lien fait intervenir la transformation intégrale de Fourier et ses généralisations. Ici, nous réexaminons la signification harmonique (ainsi qu’hilbertienne et distributionnelle) des équations fonctionnelles ayant la forme la plus simple, à savoir, celle s’appliquant pour la fonction dzêta de Riemann et les séries de Dirichlet...
Entropies of the partitions of the unit interval generated by the Farey tree
Enumerating Davenport-Schinzel sequences
Enumerating non-equivalent matrices over principal ideal domains
Enumerating quartic dihedral extensions of with signatures
In a previous paper, we have given asymptotic formulas for the number of isomorphism classes of -extensions with discriminant up to a given bound, both when the signature of the extensions is or is not specified. We have also given very efficient exact formulas for this number when the signature is not specified. The aim of this paper is to give such exact formulas when the signature is specified. The problem is complicated by the fact that the ray class characters which appear are not all genus characters....
Énumération complète des classes de formes parfaites en dimension 7
Le lecteur trouvera ici une description détaillée des méthodes et algorithmes utilisés pour démontrer qu’il n’y a que 33 classes de formes parfaites en dimension 7, ainsi qu’un tableau récapitulatif des résultats.Il trouvera, en particulier, une généralisation de l’algorithme de Voronoï appliquée en profondeur, récursivement, aux faces des domaines
Enumeration in musical theory.
Enumeration of certain sequences
Enumeration of concave integer partitions.
Enumeration of partitions by long rises, levels, and descents.
Enumeration of sequences constrained by the ratio of consecutive parts.
Enumeration of symmetric arrays with different row sums
Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes.
Enumeration of unigraphical partitions.
Episturmian morphisms and a Galois theorem on continued fractions
We associate with a word on a finite alphabet an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of . Then when we deduce, using the sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Episturmian morphisms and a Galois theorem on continued fractions
We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A|=2 we deduce, using the Sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Equal values of binary forms at integral points
Equality in Pollard's theorem on set addition of congruence classes
Equality of Dedekind sums modulo 8ℤ
Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].