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arXiv · 2011.09885

An $L^4$ maximal estimate for quadratic Weyl sums

Alex Barron
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Abstract

We show that $$\bigg\|\sup_{0 < t < 1} \big|\sum_{n=1}^{N} e^{2\pi i (n(\cdot) + n^2 t)}\big| \bigg\|_{L^{4}([0,1])} \leq C_{\epsilon} N^{3/4 + \epsilon}$$ and discuss some applications to the theory of large values of Weyl sums. This estimate is sharp for quadratic Weyl sums, up to the loss of $N^{\epsilon}$.

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Alex Barron. 2020-11-19. An $L^4$ maximal estimate for quadratic Weyl sums. https://arxiv.org/abs/2011.09885

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