Bounds for the Cubic Weyl Sum

Details Bounds for the Cubic Weyl Sum Bounds for the Cubic Weyl Sum

2009-05-12

arxiv.org/abs/0905.1869v1

Mathematics

Number Theory

Scientific paper

It is shown, subject to the abc-conjecture, that
\[\sum_{n\le N}\exp(2\pi i\alpha n^3)\ll_{\epsilon,\alpha}N^{5/7+\epsilon}\]
for any $\epsilon>0$ and any quadratic irrational $\alpha$.

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