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Répartition des points rationnels sur la cubique de Segre
Author(s) -
de la Bretèche Régis
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm001
Subject(s) - mathematics , partition (number theory) , combinatorics , humanities , art
We study the distribution of rational points on Segre's cubic defined as the locus of points x ∈ ℙ 5 such that{x 1 3 + x 2 3 + x 3 3 + x 4 3 + x 5 3 + x 6 3 = 0 ,x 1 + x 2 + x 3 + x 4 + x 5 + x 6 = 0 .In particular, we verify Manin's conjecture concerning the asymptotic behaviour of the number of non‐trivial rational points of height at most B .