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arXiv · 1401.3150

The cubic case of the main conjecture in Vinogradov's mean value theorem

Trevor D. Wooley
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Abstract

We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov's integral of degree $3$ for moments of order $2s$, establishing strongly diagonal behaviour for $1\le s\le 6$. Consequently, the main conjecture is now known to hold for the first time in a case of degree exceeding $2$.

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Trevor D. Wooley. 2014-01-14. The cubic case of the main conjecture in Vinogradov's mean value theorem. https://doi.org/10.1016/j.aim.2016.02.033

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