DC Field | Value | Language |
---|---|---|
dc.contributor.author | Im, Bo-Hae | ko |
dc.date.accessioned | 2016-09-08T00:51:31Z | - |
dc.date.available | 2016-09-08T00:51:31Z | - |
dc.date.created | 2016-09-07 | - |
dc.date.created | 2016-09-07 | - |
dc.date.issued | 2014-01 | - |
dc.identifier.citation | JOURNAL OF PURE AND APPLIED ALGEBRA, v.218, no.1, pp.18 - 26 | - |
dc.identifier.issn | 0022-4049 | - |
dc.identifier.uri | http://hdl.handle.net/10203/212934 | - |
dc.description.abstract | If k and l are coprime distinct integers, then we show that there exist infinitely many square-free integers n such that the system of two diophantine quadratic equations X-2 + knY(2) = Z(2), X-2 + lnY(2) = W-2 has infinitely many integer solutions (X, Y, Z, W) with gcd(X, Y) = 1, equivalently, the elliptic curve E-kn,E-ln : y(2) = x(x + kn)(x + ln) has positive rank over Q. (Such a pair (kn, ln) is called a strongly concordant pair.) Also, we give parametrizations of an infinite family of strongly concordant pairs (m, n) with ratio m/n = k/l and the corresponding integer solutions to X-2 + mY(2) = Z(2), X-2 + nY(2) = W-2. As an application, the result gives a parametrization of theta-congruent numbers as square-free parts of a parametrization S(t) and shows that if the number of t is an element of [1, N] such that S(t) itself is a theta-congruent number is not zero, then for all sufficiently large N, it is cN + O (N2/3+epsilon), where c > 0 and epsilon is an arbitrary small positive number. (C) 2013 Elsevier B.V. All rights reserved | - |
dc.language | English | - |
dc.publisher | ELSEVIER SCIENCE BV | - |
dc.subject | FORMS | - |
dc.title | Elliptic curves and the density of theta-congruent numbers and concordant pairs in ratios | - |
dc.type | Article | - |
dc.identifier.wosid | 000327362900002 | - |
dc.identifier.scopusid | 2-s2.0-84886639808 | - |
dc.type.rims | ART | - |
dc.citation.volume | 218 | - |
dc.citation.issue | 1 | - |
dc.citation.beginningpage | 18 | - |
dc.citation.endingpage | 26 | - |
dc.citation.publicationname | JOURNAL OF PURE AND APPLIED ALGEBRA | - |
dc.identifier.doi | 10.1016/j.jpaa.2013.04.007 | - |
dc.contributor.localauthor | Im, Bo-Hae | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | FORMS | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.