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CUBE SUM PROBLEM AND AN EXPLICIT GROSS-ZAGIER FORMULA
Cai, Li1; Shu, Jie2; Tian, Ye3
2017-06-01
Source PublicationAMERICAN JOURNAL OF MATHEMATICS
ISSN0002-9327
Volume139Issue:3Pages:785-816
AbstractA nonzero rational number is called a cube sum if it is of the form a(3) + b(3) with a, b is an element of Q(x). In this paper, we prove that for any odd integer k >= 1, there exist infinitely many cube -free odd integers n with exactly k distinct prime factors such that 2n is a cube sum (resp. not a cube sum). We present also a general construction of Heegner points and obtain an explicit Gross-Zagier formula which is used to prove the Birch and Swinnerton-Dyer conjecture for certain elliptic curves related to the cube sum problem.
Language英语
Funding ProjectChina Postdoctoral Science Foundation[2014T70067] ; 973 Program[2013CB834202] ; NSFC[11325106] ; NSFC[11321101] ; NSFC[11031004]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000401050400007
PublisherJOHNS HOPKINS UNIV PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25452
Collection数学所
Affiliation1.Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China
2.Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Cai, Li,Shu, Jie,Tian, Ye. CUBE SUM PROBLEM AND AN EXPLICIT GROSS-ZAGIER FORMULA[J]. AMERICAN JOURNAL OF MATHEMATICS,2017,139(3):785-816.
APA Cai, Li,Shu, Jie,&Tian, Ye.(2017).CUBE SUM PROBLEM AND AN EXPLICIT GROSS-ZAGIER FORMULA.AMERICAN JOURNAL OF MATHEMATICS,139(3),785-816.
MLA Cai, Li,et al."CUBE SUM PROBLEM AND AN EXPLICIT GROSS-ZAGIER FORMULA".AMERICAN JOURNAL OF MATHEMATICS 139.3(2017):785-816.
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