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An $L^4$ maximal estimate for quadratic Weyl sums (2011.09885v4)
Published 19 Nov 2020 in math.CA, math.AP, and math.NT
Abstract: We show that $$\bigg|\sup_{0 < t < 1} \big|\sum_{n=1}{N} e{2\pi i (n(\cdot) + n2 t)}\big| \bigg|{L{4}([0,1])} \leq C{\epsilon} N{3/4 + \epsilon}$$ 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 $N{\epsilon}$.