Approximations to Weyl sums
Julia Brandes (Chalmers University of Technology, Gothenburg, Sweeden)
Abstract: We study two-dimensional Weyl sums involving a k-th power and a linear term. In particular, we establish asymptotics for such sums involving lower order main terms. This allows us to draw some surprising conclusions regarding the size of such exponential sums on diagonal slices of the unit torus. As an application, we improve bounds for the fractal dimension of solutions to the Schrödinger and Airy equations. This is joint work with S. T. Parsell, K. Poulias, G. Shakan and R. C. Vaughan. Link to the paper: arxiv.org/abs/2001.05629
number theory
Audience: researchers in the topic
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