Rational points on linear slices of diagonal hypersurfaces

Jörg Brüdern (1) , Olivier Robert (2, 3)

1 Mathematische Institut
2 CTN - Combinatoire, théorie des nombres
3 ICJ - Institut Camille Jordan

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

Domaines: Théorie des nombres [math.NT]

Jörg Brüdern, Olivier Robert. Rational points on linear slices of diagonal hypersurfaces. Nagoya Mathematical Journal, 2015, 218, pp.51-100. ⟨10.1215/00277630-2891245⟩. ⟨hal-01464714⟩