About half a century ago, some authors, among others M. Kneser and G. A. Freiman, began a systematic study of what is now called “inverse additive number theory” (see [7] for a review of this theory… (More)

Later on in [2], Grekos refined the previous results, in some cases, by introducing the infimum of the radii of curvature r(Γ ) of the curve. He succeeded in showing an upper bound of the shape N(Γ )… (More)

We write Fh(N, g) for the maximum cardinality of such a set included in [1, ..., N]. Sidon sets, or B2[1] sets, are the simplest non-trivial sets of this family. They appeared naturally in the… (More)

We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if t is an integer different from 0, 1 or −1 and if A ⊂ Z/pZ is not too… (More)

We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l… (More)

We solve a problem by V. I. Arnold dealing with “how random” modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show… (More)

We consider the quantum dynamics of an electron in a periodic box of large size L, for long time scales T , in d dimensions of space, d 3. One obstacle occupying a volume 1 is present in the box, and… (More)

In this paper, we study (random) sequences of pseudo s-th powers, as introduced by Erdős and Rényi in 1960. In 1975, Goguel proved that such a sequence is almost surely not an asymptotic basis of… (More)