Approximate Carleman theorems and a Denjoy-Carleman maximum principle

We give an extension of the Denjoy-Carleman theorem, which leads to a generalization of Carleman's theorem on the unique determination of probability measures by their moments. We also give complex versions of Carleman's theorem extending Theorem 4.1 of [2]

A NUMERICAL NOTE ON UPPER BOUNDS FOR B 2 [g] SETS

International audienceSidon sets are those sets such that the sums of two of its elements never coincide. They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integers with that property. This question is now answered in a satisfactory way. Their natural generalization, called B 2 [g] sets and defined by the fact that there are at most g ways (up to reordering the summands) to represent a given integer as a sum of two elements of the set, are much more difficult to handle and not as well understood. In this article, using a numerical approach, we improve the best upper estimates on the size of a B 2 [g] set in an interval of integers in the cases g = 2, 3, 4 and 5

Spiegelungssatz: a combinatorial proof for the 4-rank

The Spiegelungssatz is an inequality between the (4)-ranks of the narrow ideal class groups of the quadratic fields (\mathbb{Q}(\sqrt{D})) and (\mathbb{Q}(\sqrt{-D})). We provide a combinatorial proof of this inequality. Our interpretation gives an affine system of equations that allows to describe precisely some equality cases

Applications of Group Representation Theory to the Easier Waring Problem

AbstractWe show how Rao and Vaserstein′s identities may be related to the groups S22 and S3. We then develop a theory that enables us to produce various identities, for any given pair (G, ϵ) of a group G and a character ϵ defined on G. When ϵ is ± 1-valued, these identities may be used to obtain upper bounds for the easier Waring problem over Z and Q. This approach may be considered as an alternative to the Tarry-Escott problem

Estimations asymptotiques du nombre de chemins Nord-Est de pente fixée et de largeur bornée

Nous étudions une quantité liée aux chemins constitués de pas Nord et Est restant sous la droite de pente d partant de l'origine. Nous donnons une estimation asymptotique de cette quantité en fonction de la largeur n de ces chemins et de la pente d, répondant ainsi à une question posée par Bernard Mourrain

Logarithmic and complex constant term identities

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamovic and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove complex and logarithmic constant term identities for the root system G_2.Comment: 26 page