arXiv 2103.088442021-03math.CAmath.AGmath.LOmath.NT

A stationary set method for estimating oscillatory integrals

Saugata Basu, Shaoming Guo, Ruixiang Zhang, Pavel Zorin-Kranich

备注：: Added an argument showing sharpness of the main result in an average sense; shared to us by Wright

英文摘要：

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 $k\ge 2$. As a consequence, we obtain sharp Fourier extension estimates for a family of monomial surfaces.

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