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

Abstract

We show that $$\Vert \underset{0<t<1}{\sup }\left|\sum _{n=1}^N{e}^{2\pi i(n(\cdot )+n^{2}t)}\right|{\Vert }_{L^4([0,1])}\le C_{\epsilon }{N}^{3/4+\epsilon }$$ 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 $N^{\epsilon }$.

Final version, to appear in IMRN

References in corpus (2)

• Hybrid bounds on two-parametric family Weyl sums along smooth curves
• On a Hybrid Version of the Vinogradov Mean Value Theorem