NOTES ON RESTRICTION THEORY IN THE PRIMES
Résumé
We study the mean x∈X p≤N upe(xp) when covers the full range [2, ∞) and X ⊂ R/Z is a well-spaced set, providing a smooth transition from the case = 2 to the case > 2 and improving on the results of J. Bourgain and of B. Green and T. Tao. A uniform Hardy-Littlewood property for the set of primes is established as well as a sharp upper bound for x∈X p≤N upe(xp) when X is small. These results are extended to primes in any interval in a last section, provided the primes are numerous enough therein.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)