Density of modular forms with transcendental zeros
DC Field | Value | Language |
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dc.contributor.author | Choi, Dohoon | - |
dc.contributor.author | Lee, Youngmin | - |
dc.contributor.author | Lim, Subong | - |
dc.date.accessioned | 2022-02-25T09:41:13Z | - |
dc.date.available | 2022-02-25T09:41:13Z | - |
dc.date.created | 2022-02-09 | - |
dc.date.issued | 2021-08-15 | - |
dc.identifier.issn | 0022-247X | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/136846 | - |
dc.description.abstract | For an even positive integer k, let M-k,M-Z(SL2(Z)) be the set of modular forms of weight k on SL2(Z) with integral Fourier coefficients. Let M-k,Z(tran) (SL2(Z)) be the subset of M-k,M-Z(SL2(Z)) consisting of modular forms with only transcendental zeros on the upper half plane H except all elliptic points of SL2(Z). For a modular form f(z) = Sigma(infinity)(n=0) a(f)(n)(e2 pi inz) of weight k(f), let omega(f) := Sigma(rk(f))(n=0) |a(f) (n)|, where r(k(f)) = dim(C) M-k(f),M-Z(SL2(Z)) circle times C -1. In this paper, we prove that if k = 12 or k > 16, then #{f is an element of M-k,Z(tran) (SL2(Z)) : omega(f) <= X}/#{f is an element of M-k,M-Z(SL2(Z)) : omega(f) <= X} = 1 - alpha k/X = O(1/X-2) as X ->infinity where alpha(k) denotes the sum of the volumes of certain polytopes. Moreover, if we let M-Z = (Uk =0Mk,Z)-M-infinity(SL2(Z)) (resp. M-Z(tran)= (Uk=0Mk,Ztran)-M-infinity (SL2(Z))) and phi is a monotone increasing function on R+ such that phi(x + 1) - phi(x) >= Cx(2) for some positive number C, then we prove lim(X ->infinity) #{f is an element of M-Z(tran) : omega(f) + phi(k(f)) <= X}/#{f is an element of M-Z : omega(f) + phi(k(f)) <= X} = 1. (C) 2021 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.title | Density of modular forms with transcendental zeros | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Choi, Dohoon | - |
dc.identifier.doi | 10.1016/j.jmaa.2021.125141 | - |
dc.identifier.scopusid | 2-s2.0-85102639076 | - |
dc.identifier.wosid | 000641169200007 | - |
dc.identifier.bibliographicCitation | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.500, no.2 | - |
dc.relation.isPartOf | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | - |
dc.citation.title | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | - |
dc.citation.volume | 500 | - |
dc.citation.number | 2 | - |
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, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordAuthor | Density | - |
dc.subject.keywordAuthor | Modular forms | - |
dc.subject.keywordAuthor | Transcendental zeros | - |
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