Rational points on linear slices of diagonal hypersurfaces

Abstract : An asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. The formula is proved via the Hardy-Littlewood method, and along the way we establish two new results on Weyl sums that are of some independent interest
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Jörg Brüdern, Olivier Robert. Rational points on linear slices of diagonal hypersurfaces. Nagoya Mathematical Journal, Duke University Press, 2015, pp.51-100. ⟨http:/www.cambridge.org⟩. ⟨10.1215/00277630-2891245⟩. ⟨hal-01464714⟩

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