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Article Dans Une Revue Israel Journal of Mathematics Année : 2023

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.
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hal-03381428 , version 1 (16-10-2021)

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Olivier Ramaré. NOTES ON RESTRICTION THEORY IN THE PRIMES. Israel Journal of Mathematics, 2023, ⟨10.1007/s11856-023-2586-5⟩. ⟨hal-03381428⟩
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