DC Field | Value | Language |
---|---|---|
dc.contributor.author | Im, Bo-Hae | ko |
dc.date.accessioned | 2016-09-08T00:51:43Z | - |
dc.date.available | 2016-09-08T00:51:43Z | - |
dc.date.created | 2016-09-07 | - |
dc.date.created | 2016-09-07 | - |
dc.date.issued | 2013-02 | - |
dc.identifier.citation | JOURNAL OF NUMBER THEORY, v.133, no.2, pp.492 - 500 | - |
dc.identifier.issn | 0022-314X | - |
dc.identifier.uri | http://hdl.handle.net/10203/212936 | - |
dc.description.abstract | Let K be a number field and E-i/K an elliptic curve defined over K for i = 1, 2, 3, 4. We prove that there exists a number field L containing K such that there are infinitely many d(k) is an element of L-x/(L-x)(2) such that E-i(dk)(L) has positive rank, equivalently all four elliptic curves E-i have growth of the rank over each of quadratic extensions L-k := L(root d(k)), more strongly, for any, i(1), i(2), ... , i(m). rank (E-i(l(i1) .. L-m)) > rank(E-i(L-i1 ... Lim-1)) > ... >rank(E-i(L-i1)) > rank(E-i(L)). We also prove that if each elliptic curve E-i for i = 1, 2,3 can be written in Legendre form over a cubic extension K of a number field k, then there are infinitely many d is an element of k(x)/(k(x))(2) such that E-i(d)(K) for i = 1, 2, 3 is of positive rank. (C) 2012 Elsevier Inc. All rights reserved | - |
dc.language | English | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject | FIELDS | - |
dc.title | Positive rank quadratic twists of four elliptic curves | - |
dc.type | Article | - |
dc.identifier.wosid | 000311769200010 | - |
dc.identifier.scopusid | 2-s2.0-84867664964 | - |
dc.type.rims | ART | - |
dc.citation.volume | 133 | - |
dc.citation.issue | 2 | - |
dc.citation.beginningpage | 492 | - |
dc.citation.endingpage | 500 | - |
dc.citation.publicationname | JOURNAL OF NUMBER THEORY | - |
dc.identifier.doi | 10.1016/j.jnt.2012.08.023 | - |
dc.contributor.localauthor | Im, Bo-Hae | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Elliptic curve | - |
dc.subject.keywordAuthor | Quadratic twist | - |
dc.subject.keywordPlus | FIELDS | - |
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