Effective construction of Hilbert modular forms of half-integral weight
Resumen:
Given a Hilbert cuspidal newform g we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted L-series of g by fundamental discriminants. The family is parametrized by quadratic conditions on the primes dividing the level of g, where each form has coefficients supported on the discriminants satisfying the conditions. These modular forms are given as generalized theta series and thus their coefficients can be effectively computed. By considering skew-holomorphic forms of half-integral weight our construction works over arbitrary totally real number fields, except that in the case of odd degree the square levels are excluded. It includes all discriminants except those divisible by primes whose square divides the level.
| 2022 | |
| Number Theory | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38376 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522796831506432 |
|---|---|
| author | Sirolli, Nicolás |
| author2 | Tornaría, Gonzalo |
| author2_role | author |
| author_facet | Sirolli, Nicolás Tornaría, Gonzalo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Sirolli Nicolás Tornaría Gonzalo, Universidad de la República (Uruguay). Facultad de Ciencias. |
| dc.creator.none.fl_str_mv | Sirolli, Nicolás Tornaría, Gonzalo |
| dc.date.accessioned.none.fl_str_mv | 2023-07-24T21:50:40Z |
| dc.date.available.none.fl_str_mv | 2023-07-24T21:50:40Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | Given a Hilbert cuspidal newform g we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted L-series of g by fundamental discriminants. The family is parametrized by quadratic conditions on the primes dividing the level of g, where each form has coefficients supported on the discriminants satisfying the conditions. These modular forms are given as generalized theta series and thus their coefficients can be effectively computed. By considering skew-holomorphic forms of half-integral weight our construction works over arbitrary totally real number fields, except that in the case of odd degree the square levels are excluded. It includes all discriminants except those divisible by primes whose square divides the level. |
| dc.description.es.fl_txt_mv | Publicado también como: Mathematische Zeitschrift, 2022, 302: 2513–2543. DOI: 10.1007/s00209-022-03140-2 |
| dc.format.extent.es.fl_str_mv | 30 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Sirolli, N y Tornaría, G. "Effective construction of Hilbert modular forms of half-integral weight" [Preprint]. Publicado en: Mathematics (Number Theory). 2022, arXiv:2107.04483v2, oct 2022, pp. 1-30 |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2107.04483 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/38376 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Number Theory), arXiv: 2107.04483v2, oct 2022, pp. 1-30 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Number Theory |
| dc.title.none.fl_str_mv | Effective construction of Hilbert modular forms of half-integral weight |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Publicado también como: Mathematische Zeitschrift, 2022, 302: 2513–2543. DOI: 10.1007/s00209-022-03140-2 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_c70a4b70322dbbcdce8e0d6ad4360d30 |
| identifier_str_mv | Sirolli, N y Tornaría, G. "Effective construction of Hilbert modular forms of half-integral weight" [Preprint]. Publicado en: Mathematics (Number Theory). 2022, arXiv:2107.04483v2, oct 2022, pp. 1-30 10.48550/arXiv.2107.04483 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/38376 |
| publishDate | 2022 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Sirolli NicolásTornaría Gonzalo, Universidad de la República (Uruguay). Facultad de Ciencias.2023-07-24T21:50:40Z2023-07-24T21:50:40Z2022Sirolli, N y Tornaría, G. "Effective construction of Hilbert modular forms of half-integral weight" [Preprint]. Publicado en: Mathematics (Number Theory). 2022, arXiv:2107.04483v2, oct 2022, pp. 1-30https://hdl.handle.net/20.500.12008/3837610.48550/arXiv.2107.04483Publicado también como: Mathematische Zeitschrift, 2022, 302: 2513–2543. DOI: 10.1007/s00209-022-03140-2Given a Hilbert cuspidal newform g we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted L-series of g by fundamental discriminants. The family is parametrized by quadratic conditions on the primes dividing the level of g, where each form has coefficients supported on the discriminants satisfying the conditions. These modular forms are given as generalized theta series and thus their coefficients can be effectively computed. By considering skew-holomorphic forms of half-integral weight our construction works over arbitrary totally real number fields, except that in the case of odd degree the square levels are excluded. It includes all discriminants except those divisible by primes whose square divides the level.Submitted by Egaña Florencia (florega@gmail.com) on 2023-07-24T18:25:08Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2107.04483.pdf: 798365 bytes, checksum: a8a0a5d9c1260ed574245403053d1d64 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-07-24T18:30:53Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2107.04483.pdf: 798365 bytes, checksum: a8a0a5d9c1260ed574245403053d1d64 (MD5)Made available in DSpace by Seroubian Mabel (mabel.seroubian@seciu.edu.uy) on 2023-07-24T21:50:40Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2107.04483.pdf: 798365 bytes, checksum: a8a0a5d9c1260ed574245403053d1d64 (MD5) Previous issue date: 202230 h.application/pdfenengarXivMathematics (Number Theory), arXiv: 2107.04483v2, oct 2022, pp. 1-30Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Number TheoryEffective construction of Hilbert modular forms of half-integral weightPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaSirolli, NicolásTornaría, GonzaloLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/38376/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/38376/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-838767http://localhost:8080/xmlui/bitstream/20.500.12008/38376/3/license_text1df05be915d5c44b48b8b2e7a082b91aMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Effective construction of Hilbert modular forms of half-integral weight Sirolli, Nicolás Number Theory |
| status_str | submittedVersion |
| title | Effective construction of Hilbert modular forms of half-integral weight |
| title_full | Effective construction of Hilbert modular forms of half-integral weight |
| title_fullStr | Effective construction of Hilbert modular forms of half-integral weight |
| title_full_unstemmed | Effective construction of Hilbert modular forms of half-integral weight |
| title_short | Effective construction of Hilbert modular forms of half-integral weight |
| title_sort | Effective construction of Hilbert modular forms of half-integral weight |
| topic | Number Theory |
| url | https://hdl.handle.net/20.500.12008/38376 |
