2021/11/08 by Jianya Liu, Tingting Wen, Liu, Jianya +3
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.2111.04341
arxiv created 2021/11/08 · arxiv updated 2021/11/09
Let S Q denote x 3 = Q(y 1 ,. .. , y m)z where Q is a primitive positive definite quadratic form in m variables with integer coefficients. This S Q ranges over a class of singular cubic hypersurfaces as Q varies. For S Q we prove (i) Manin's conjecture is true if Q is locally determined with 2 | m and m 4; (ii) in general Manin's conjecture is true up to a leading constant if 2 | m and m 6.