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arXiv · 1401.7152

Mean value estimates for odd cubic Weyl sums

Trevor D. Wooley
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Abstract

We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $αx^3+βx$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.

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Trevor D. Wooley. 2014-01-28. Mean value estimates for odd cubic Weyl sums. https://doi.org/10.1112/blms%2Fbdv066

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