2014/01/09 by Ciprian Demeter, Demeter, Ciprian · 10 citations
Mathematics · Physics and Astronomy · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Appeal #Applied mathematics #Black Holes and Theoretical Physics #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Geometry #Incidence (geometry) #Irrational number #Law #Mathematics #Phenomenon #Physics #Pure mathematics #Quantum mechanics #Torus #math.AP #math.CA #math.CO
paper · pdf · doi:10.48550/arxiv.1401.1873
published in arXiv (Cornell University) (Cornell University)
arxiv created 2014/01/09 · openalex publication_date 2014/01/09 · arxiv updated 2014/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the interplay between the discrete restriction phenomenon and incidence theory. Two angles are explored. One is a refinement of the machinery developed by Thomas Wolff, which when combined with a recent subcritical estimate of Bourgain leads to new Strichartz estimates for irrational tori. The other one connects various additive energies with the Szemerédi-Trotter Theorem. The combination of the two approaches recovers the best known Strichartz estimates for the classical torus in dimensions n≥ 3, without any appeal to number theory.