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Kim, Tae Kyung
기하학 수리물리 연구단
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A conjecture of Gross and Zagier: Case e (Q)tor ≃ Z/2Z ⊕ Z/2Z, Z/2Z ⊕z/4Z or Z/2Z ⊕ Z/6Z

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dc.contributor.authorByeon D.-
dc.contributor.authorKim, Taekyung-
dc.contributor.authorYhee D.-
dc.date.accessioned2020-12-22T02:49:58Z-
dc.date.accessioned2020-12-22T02:49:58Z-
dc.date.available2020-12-22T02:49:58Z-
dc.date.available2020-12-22T02:49:58Z-
dc.date.created2020-06-29-
dc.date.issued2020-08-
dc.identifier.issn1793-0421-
dc.identifier.urihttps://pr.ibs.re.kr/handle/8788114/7718-
dc.description.abstract© 2020 World Scientific Publishing Company. Let E be an elliptic curve defined over Q of conductor N, c the Manin constant of E, and m the product of Tamagawa numbers of E at prime divisors of N. Let K be an imaginary quadratic field where all prime divisors of N split in K, PK the Heegner point in E(K), and III(E/K) the Shafarevich-Tate group of E over K. Let 2uK be the number of roots of unity contained in K. Gross and Zagier conjectured that if PK has infinite order in E(K), then the integer c . m . uK .|III(E/K)|1 2 is divisible by |E(Q)tor|. In this paper, we show that this conjecture is true if E (Q)tor ≃ Z/2Z ⊕ Z/2Z, Z/2Z ⊕Z/4Z or Z/2Z ⊕ Z/6Z-
dc.description.uri1-
dc.language영어-
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD-
dc.subjectElliptic curves-
dc.subjectManin constant-
dc.subjectShafarevich-Tate group-
dc.subjectTamagawa number-
dc.titleA conjecture of Gross and Zagier: Case e (Q)tor ≃ Z/2Z ⊕ Z/2Z, Z/2Z ⊕z/4Z or Z/2Z ⊕ Z/6Z-
dc.typeArticle-
dc.type.rimsART-
dc.identifier.wosid000562048300009-
dc.identifier.scopusid2-s2.0-85084797175-
dc.identifier.rimsid72251-
dc.contributor.affiliatedAuthorKim, Taekyung-
dc.identifier.doi10.1142/S1793042120500827-
dc.identifier.bibliographicCitationINTERNATIONAL JOURNAL OF NUMBER THEORY, v.16, no.7, pp.1567 - 1572-
dc.citation.titleINTERNATIONAL JOURNAL OF NUMBER THEORY-
dc.citation.volume16-
dc.citation.number7-
dc.citation.startPage1567-
dc.citation.endPage1572-
dc.description.journalClass1-
dc.description.journalRegisteredClassscie-
dc.description.journalRegisteredClassscopus-
dc.subject.keywordAuthorElliptic curves-
dc.subject.keywordAuthorManin constant-
dc.subject.keywordAuthorShafarevich-Tate group-
dc.subject.keywordAuthorTamagawa number-
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Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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