On restriction of exponential sums to hypersurfaces with zero curvature

2021/10/21 by Ciprian Demeter, Demeter, Ciprian
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.11224

openalex publication_date 2021/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove essentially sharp bounds for the L^p restriction of weighted Gauss sums to monomial curves. Getting the L² upper bound combines the TT^* method for matrices with the first and second derivative test for exponential sums. The matching lower bound follows via constructive interference on short blocks of integers, near the critical point of the phase function. This method is used to make the broader point that restriction to hypersurfaces is really sensitive to curvature. Our results here complement earlier results by the author and Langowski.

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