A stationary set method for estimating oscillatory integrals

2021/03/16 by Saugata Basu, Shaoming Guo, Basu, Saugata +5 · 3 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2103.08844

openalex publication_date 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarry's problems in dimension two for every degree k≥ 2. As a consequence, we obtain sharp Fourier extension estimates for a family of monomial surfaces.

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