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 d...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.展开更多
Let t（G） be the number of unitary factors of finite abelian group G. In this paper we prove T（x）=∑<sub>(</sub>G≤（）t（G） =main terms+O(x<sup>(</sup>（1+2k）/（3+4k）for any exponent pa...Let t（G） be the number of unitary factors of finite abelian group G. In this paper we prove T（x）=∑<sub>(</sub>G≤（）t（G） =main terms+O(x<sup>(</sup>（1+2k）/（3+4k）for any exponent pair （k, 1/2+2K）. which improves on the exponent 9/25 obtained by Xiaodong Cao and the author.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971476).
文摘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.
基金Supported by MCME and Natural Science Foundation of Shandong Province(Grant No. Q98A02110)
文摘Let t（G） be the number of unitary factors of finite abelian group G. In this paper we prove T（x）=∑<sub>(</sub>G≤（）t（G） =main terms+O(x<sup>(</sup>（1+2k）/（3+4k）for any exponent pair （k, 1/2+2K）. which improves on the exponent 9/25 obtained by Xiaodong Cao and the author.
