A parametrization of $\theta$-congruent numbers with many prime factors and with prescribed prime factors

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dc.contributor.authorIm, Bo-Haeko
dc.contributor.authorKim, HanSolko
dc.date.accessioned2018-07-24T02:24:09Z-
dc.date.available2018-07-24T02:24:09Z-
dc.date.created2018-04-18-
dc.date.created2018-04-18-
dc.date.created2018-04-18-
dc.date.issued2018-06-
dc.identifier.citationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.462, no.1, pp.407 - 427-
dc.identifier.issn0022-247X-
dc.identifier.urihttp://hdl.handle.net/10203/244047-
dc.description.abstractLet theta be a real number such that 0 < theta < pi and cos theta is an element of Q. For each positive integer n, we give a parametrization S-n (alpha) whose square-free part N-n (alpha) for each negative integer alpha is a theta-congruent number with many prime factors including any given primes (especially, at least n prime factors that are guaranteed to appear) by showing the positivity of the rank of the corresponding theta-congruent number elliptic curve over Q. Especially, we show that if a given odd prime p > 2n is near 2n, then p appears as a factor of N-n(alpha) very often as a varies all over negative integers by proving that the probability of the set of all negative integers alpha such that p divides N-n (alpha) is 2n+1/p+1. (C) 2018 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titleA parametrization of $\theta$-congruent numbers with many prime factors and with prescribed prime factors-
dc.typeArticle-
dc.identifier.wosid000435065200026-
dc.identifier.scopusid2-s2.0-85044849901-
dc.type.rimsART-
dc.citation.volume462-
dc.citation.issue1-
dc.citation.beginningpage407-
dc.citation.endingpage427-
dc.citation.publicationnameJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS-
dc.identifier.doi10.1016/j.jmaa.2018.01.068-
dc.contributor.localauthorIm, Bo-Hae-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorElliptic curve-
dc.subject.keywordAuthorCongruent number-
dc.subject.keywordAuthortheta-congruent number-
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MA-Journal Papers(저널논문)
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