On L¹² square root cancellation for exponential sums associated with nondegenerate curves in \mathbb R⁴

2021/01/20 by Demeter, Ciprian · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.08220

Abstract

We prove sharp L¹² estimates for exponential sums associated with nondegenerate curves in \mathbb R⁴. We place Bourgain's progress on the Lindel"of hypothesis in a larger framework that contains a continuum of estimates of different flavor. We enlarge the spectrum of methods by combining decoupling with quadratic Weyl sum estimates, to address new cases of interest. All results are proved in the general framework of real analytic curves.

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