Pairs of eta-quotients with dual weights and their applications
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choi, Dohoon | - |
dc.contributor.author | Kim, Byungchan | - |
dc.contributor.author | Lim, Subong | - |
dc.date.accessioned | 2021-09-01T02:44:10Z | - |
dc.date.available | 2021-09-01T02:44:10Z | - |
dc.date.created | 2021-06-19 | - |
dc.date.issued | 2019-10-15 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/62508 | - |
dc.description.abstract | Let D be the differential operator defined by D := 1/2 pi i d/dz. This induces a map Dk+1 : M--k(!)(Gamma(0)(N)) -> M-k+2(!)(Gamma(0)(N)), where M-k(!)(Gamma(0)(N)) is the space of weakly holomorphic modular forms of weight k on Gamma(0)(N). The operator Dk+1 plays important roles in the theory of Eichler-Shimura cohomology and harmonic weak Maass forms. On the other hand, eta-quotients are fundamental objects in the theory of modular forms and partition functions. In this paper, we show that the structure of eta-quotients is very rarely preserved under the map Dk+1 between dual spaces M--k(!) (Gamma(0)(N)) and M-k+2(!)(Gamma(0)(N)). More precisely, we classify dual pairs (f, Dk+1 f) under the map Dk+1 such that f is an eta-quotient and Dk+l f is a non-zero constant multiple of an eta-quotient. When the levels are square-free, we give the complete classification of such pairs. In general, we find a necessary condition for such pairs: the weight of the primitive eta-quotient f(z) = eta(d(i1) z)(b1) ... eta(d(it) z)(bt) is less than or equal to 4 and every prime divisor of each d(i) is less than 11. We also give various applications of these classifications. In particular, we find all eta-quotients of weight 2 and square-free level N such that they are in the Eisenstein space for Gamma(0)(N). To prove our main theorems, we use various combinatorial properties of a Latin square matrix whose rows and columns are exactly divisors of N. (C) 2019 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject | MOCK MODULAR-FORMS | - |
dc.subject | WEAK MAASS FORMS | - |
dc.subject | LAMBERT SERIES | - |
dc.subject | OPERATORS | - |
dc.subject | SPACES | - |
dc.title | Pairs of eta-quotients with dual weights and their applications | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Choi, Dohoon | - |
dc.identifier.doi | 10.1016/j.aim.2019.106779 | - |
dc.identifier.scopusid | 2-s2.0-85071137224 | - |
dc.identifier.wosid | 000487567200016 | - |
dc.identifier.bibliographicCitation | ADVANCES IN MATHEMATICS, v.355 | - |
dc.relation.isPartOf | ADVANCES IN MATHEMATICS | - |
dc.citation.title | ADVANCES IN MATHEMATICS | - |
dc.citation.volume | 355 | - |
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.keywordPlus | MOCK MODULAR-FORMS | - |
dc.subject.keywordPlus | WEAK MAASS FORMS | - |
dc.subject.keywordPlus | LAMBERT SERIES | - |
dc.subject.keywordPlus | OPERATORS | - |
dc.subject.keywordPlus | SPACES | - |
dc.subject.keywordAuthor | Eta-quotient | - |
dc.subject.keywordAuthor | D-operator | - |
dc.subject.keywordAuthor | Lambert series | - |
dc.subject.keywordAuthor | Latin matrix | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
(02841) 서울특별시 성북구 안암로 14502-3290-1114
COPYRIGHT © 2021 Korea University. All Rights Reserved.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.