Decoupling for complex curves and improved decoupling for the cubic moment curve

2023/02/21 by Robert Schippa, Schippa, Robert
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2302.10884

openalex publication_date 2023/02/21 · openalex created_date 2023/02/24 · openalex updated_date 2026/07/28

Abstract

We prove sharp ℓ²-decoupling inequalities for non-degenerate complex curves via the bilinear argument due to Guo--Li--Yung--Zorin-Kranich, which in turn is inspired by the efficient congruencing argument of Wooley. Secondly, quantifying the iteration in the cubic case, we obtain a logarithmic refinement of the decoupling inequality for the cubic moment curve.

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