Manin’s conjecture for a class of singular cubic hypersurfaces  

作　　者：Wenguang ZHAI 

机构地区：[1]Department of Mathematics,China University of Mining and Technology,Beijing,100083,China

出　　处：《Frontiers of Mathematics in China》2022年第6期1089-1132,共44页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11971476).

摘　　要：Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.

关 键 词：Manin’s conjecture quadratic form asymptotic formula divisor problem exponential sum 

分 类 号：O17[理学—数学]