Mostrar el registro sencillo del ítem
dc.date.available
2023-01-20T19:21:38Z
dc.identifier.citation
Sirolli, Nicolás Martín; Tornaría López, Gonzalo; (2023): Hilbert modular forms of half-integral weight. Consejo Nacional de Investigaciones Científicas y Técnicas. (dataset). http://hdl.handle.net/11336/185179
dc.identifier.uri
http://hdl.handle.net/11336/185179
dc.description.abstract
These files are the result of using the main result from "Nicolás Sirolli and Gonzalo Tornaría, Effective construction of Hilbert modular forms of half-integral weight" for computing the central values twisted L-series attached to Hilbert modular forms.
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.title
Hilbert modular forms of half-integral weight
dc.type
dataset
dc.date.updated
2023-01-19T19:48:46Z
dc.description.fil
Fil: Sirolli, Nicolás Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Tornaría López, Gonzalo. Universidad de la República. Facultad de Ciencias; Uruguay
dc.datacite.PublicationYear
2023
dc.datacite.Creator
Sirolli, Nicolás Martín
dc.datacite.Creator
Tornaría López, Gonzalo
dc.datacite.affiliation
Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"
dc.datacite.affiliation
Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática
dc.datacite.affiliation
Universidad de la República. Facultad de Ciencias
dc.datacite.publisher
Consejo Nacional de Investigaciones Científicas y Técnicas
dc.datacite.subject
Matemática Pura
dc.datacite.subject
Matemáticas
dc.datacite.subject
CIENCIAS NATURALES Y EXACTAS
dc.datacite.date
21/08/2021-21/08/2021
dc.datacite.DateType
Creado
dc.datacite.language
eng
dc.datacite.AlternateIdentifierType
info:eu-repo/semantics/altIdentifier/url/http://www.cmat.edu.uy/cnt/hmf2/
dc.datacite.version
1.0
dc.datacite.description
Each of the files corresponds to a Hilbert modular form g, and is named after the label of g in the LMFDB database.
The files contain a header with commented information, including the quaternion algebra and the order R used in each case, along with the following lines:
The first line contains a list with information about the quaternionic modular form φ in correspondence with g.
The elements of this list are tuples (cI,LI) corresponding to representatives I for the right ideal classes for R.
Here LI is a basis over the rational integers for the left order of I and cI is the I-th coefficient of φ, divided by the order of the torsion group of LI.
The second line contains a list of tuples (p,pv), where p ranges over the prime divisors of the level of g, and pv is the auxiliary vector used for defining the weight function at p.
The prime p is described by giving a basis for it over the rational integers.
The subsequent lines correspond to the different admissible functions gamma; they are preceeded by a commented line describing the function in question.
Each line contains a list [l,lvec,cvs].
Here l is the auxiliary parameter, and lvec the auxilary vector for computing the weight function at l.
Finally, cvs is the list containing central values and Fourier coefficients, which we describe with detail below.
The main object of these computations are the lists cvs.
Each of these lists is made out of tuples (N,cvsN), which appear in the list sorted increasingly according to the absolute value of N.
Here cvsN is a list of tuples which have entries (D,λ(D),LD).
These entries include every integral D of type γ such that (D,O) is a fundamental discriminant having norm equal to N, and such that -lD belongs to a certain Shintani cone which serves as fundamental domain for the action of the group (Ox)2 acting on F+. Here the absolute value of N goes up to the precision Nmax indicated in the header.
Finally,
λ(D) = λ(D,O;f)
LD = L(1/2,g⊗χD)
are respectively the (D,O)-th Fourier coefficient of the theta series f corresponding to g and the central value of the L-series twisted by χD. They satisfy the central values formula
L(1/2,g⊗χD) = 2ω(D,N) · <g,g> · cg,γ / |D|1/2 · |λ(D,O;f)|2 / <f,f>.
See Theorem A from our article for notation and details.
dc.datacite.DescriptionType
Tabla de contenidos
dc.relationtype.isSourceOf
http://hdl.handle.net/11336/213656
dc.subject.keyword
Half-integral
dc.subject.keyword
Hilbert
dc.subject.keyword
Modular
dc.subject.keyword
Central values
dc.datacite.resourceTypeGeneral
dataset
dc.conicet.datoinvestigacionid
4387
dc.conicet.justificacion
Los datos se obtuvieron realizando cálculos en una computadora.
dc.datacite.formatedDate
2021
Archivos del conjunto de datos
Archivo
Notas de uso
Tamaño