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- Publisher Website: 10.1007/s40993-020-00235-9
- Scopus: eid_2-s2.0-85099352828
- WOS: WOS:000607540100001
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Article: Sign Changes of Fourier Coefficients of Cusp Forms of Half-Integral Weight Over Split and Inert Primes in Quadratic Number Fields
Title | Sign Changes of Fourier Coefficients of Cusp Forms of Half-Integral Weight Over Split and Inert Primes in Quadratic Number Fields |
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Authors | |
Keywords | Half-integral weight modular forms Sign changes Fourier coefficients Quadratic number fields Quadratic forms |
Issue Date | 2021 |
Publisher | Springer. The Journal's web site is located at https://www.springer.com/journal/40993 |
Citation | Research in Number Theory, 2021, v. 7, p. article no. 10 How to Cite? |
Abstract | In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class tZ2, we investigate the sign changes in the tp2-th coefficient as p runs through the split or inert primes over the ring of integers in a quadratic extension of the rationals. We show that infinitely many sign changes occur in both sets of primes when there exists a prime dividing the discriminant of the field which does not divide the level of the cusp form and find an explicit condition that determines whether sign changes occur when every prime dividing the discriminant also divides the level. |
Persistent Identifier | http://hdl.handle.net/10722/300591 |
ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.595 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | HE, Z | - |
dc.contributor.author | Kane, B | - |
dc.date.accessioned | 2021-06-18T14:54:12Z | - |
dc.date.available | 2021-06-18T14:54:12Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Research in Number Theory, 2021, v. 7, p. article no. 10 | - |
dc.identifier.issn | 2363-9555 | - |
dc.identifier.uri | http://hdl.handle.net/10722/300591 | - |
dc.description.abstract | In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class tZ2, we investigate the sign changes in the tp2-th coefficient as p runs through the split or inert primes over the ring of integers in a quadratic extension of the rationals. We show that infinitely many sign changes occur in both sets of primes when there exists a prime dividing the discriminant of the field which does not divide the level of the cusp form and find an explicit condition that determines whether sign changes occur when every prime dividing the discriminant also divides the level. | - |
dc.language | eng | - |
dc.publisher | Springer. The Journal's web site is located at https://www.springer.com/journal/40993 | - |
dc.relation.ispartof | Research in Number Theory | - |
dc.rights | Accepted Manuscript (AAM) This is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI] | - |
dc.subject | Half-integral weight modular forms | - |
dc.subject | Sign changes | - |
dc.subject | Fourier coefficients | - |
dc.subject | Quadratic number fields | - |
dc.subject | Quadratic forms | - |
dc.title | Sign Changes of Fourier Coefficients of Cusp Forms of Half-Integral Weight Over Split and Inert Primes in Quadratic Number Fields | - |
dc.type | Article | - |
dc.identifier.email | Kane, B: bkane@hku.hk | - |
dc.identifier.authority | Kane, B=rp01820 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s40993-020-00235-9 | - |
dc.identifier.scopus | eid_2-s2.0-85099352828 | - |
dc.identifier.hkuros | 323018 | - |
dc.identifier.volume | 7 | - |
dc.identifier.spage | article no. 10 | - |
dc.identifier.epage | article no. 10 | - |
dc.identifier.isi | WOS:000607540100001 | - |
dc.publisher.place | Germany | - |