Independence between coefficients of two modular forms
DC Field | Value | Language |
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dc.contributor.author | Choi, Dohoon | - |
dc.contributor.author | Lim, Subong | - |
dc.date.accessioned | 2021-09-01T08:23:57Z | - |
dc.date.available | 2021-09-01T08:23:57Z | - |
dc.date.created | 2021-06-18 | - |
dc.date.issued | 2019-09 | - |
dc.identifier.issn | 0022-314X | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/63446 | - |
dc.description.abstract | Let k be an even integer and Sk be the space of cusp forms of weight k on SL2(Z). Let S = circle plus S-k is an element of 2z(k). For f, g is an element of S, we let R(f, g) be the set of ratios of the Fourier coefficients of f and g defined by R(f, g) := {x is an element of P-1 (C) vertical bar x = [a(f)(p) : a(g) (p)] for some prime p}, where a(f)(n) (resp. a(g)(n)) denotes the nth Fourier coefficient of f (resp. g). In this paper, we prove that if f and g are nonzero and R(f, g) is finite, then f = cg for some constant c. This result is extended to the space of weakly holomorphic modular forms on SL2(Z). We apply it to study the number of representations of a positive integer by a quadratic form. (C) 2019 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.title | Independence between coefficients of two modular forms | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Choi, Dohoon | - |
dc.identifier.doi | 10.1016/j.jnt.2019.01.005 | - |
dc.identifier.scopusid | 2-s2.0-85061818821 | - |
dc.identifier.wosid | 000470343700014 | - |
dc.identifier.bibliographicCitation | JOURNAL OF NUMBER THEORY, v.202, pp.298 - 315 | - |
dc.relation.isPartOf | JOURNAL OF NUMBER THEORY | - |
dc.citation.title | JOURNAL OF NUMBER THEORY | - |
dc.citation.volume | 202 | - |
dc.citation.startPage | 298 | - |
dc.citation.endPage | 315 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordAuthor | Fourier coefficient | - |
dc.subject.keywordAuthor | Modular form | - |
dc.subject.keywordAuthor | Galois representation | - |
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