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Pré-Publication, Document De Travail Année : 2024

Equidistribution of nilflows and bounds on Weyl sums

Résumé

We prove an effective equidistribution result for a class of higher step nilflows, called filiform nilflows, and derive bounds on Weyl sums for higher degree polynomials with a power saving comparable to the best known, derived by J. Bourgain, C. Demeter and L. Guth and by T. Wooley from their proof of Vinogradov Main Conjecture. Our argument is based on ideas from dynamical systems (cohomological equations, invariant distributions) and on non-Abelian harmonic analysis.

Dates et versions

hal-04404261 , version 1 (18-01-2024)

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Livio Flaminio, Giovanni Forni. Equidistribution of nilflows and bounds on Weyl sums. 2024. ⟨hal-04404261⟩
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