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Rational points on a class of cubic hypersurfaces.
- Source :
-
Forum Mathematicum . Jul2024, p1. 26p. - Publication Year :
- 2024
-
Abstract
- Let r ⩾ 3 r\geqslant 3 be an integer and 푄 any positive definite quadratic form in 푟 variables. We establish asymptotic formulae with power-saving error terms for the number of rational points of bounded height on singular hypersurfaces S Q S_{Q} defined by x 3 = Q ( y 1 , … , y r ) z x^{3}=Q(y_{1},\dots,y_{r})z . This confirms Manin’s conjecture for any S Q S_{Q} . Our proof is based on analytic methods, and uses some estimates for character sums and moments of 퐿-functions. In particular, one of the ingredients is Siegel’s mass formula in the argument for the case r = 3 r=3 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09337741
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 178653778
- Full Text :
- https://doi.org/10.1515/forum-2023-0394