Mostrar el registro sencillo del ítem

dc.contributor.author
Bruggeman, Roelof W.  
dc.contributor.author
Miatello, Roberto Jorge  
dc.date.available
2017-01-13T20:49:20Z  
dc.date.issued
2013-12  
dc.identifier.citation
Bruggeman, Roelof W.; Miatello, Roberto Jorge; Eigenvalues of Hecke operators on Hilbert modular groups; International Press Boston; Asian Journal of Mathematics; 17; 4; 12-2013; 729-757  
dc.identifier.issn
1093-6106  
dc.identifier.uri
http://hdl.handle.net/11336/11335  
dc.description.abstract
Abstract. Let F be a totally real field, let I be a nonzero ideal of the ring of integers OF Q of F, let 0(I) be the congruence subgroup of Hecke type of G = dj =1 SL2(R) embedded diagonally in G, and let be a character of 0(I) of the form ac b d = (d), where d 7! (d) is a character of OF modulo I. For a finite subset P of prime ideals p not dividing I, we consider the ring HI , generated by the Hecke operators T(p2), p 2 P (see x3.2) acting on (; )- automorphic forms on G. Given the cuspidal space L2;cusp 0(I)nG; , we let V$ run through an orthogonal system of irreducible G-invariant subspaces so that each V$ is invariant under HI . For each 1 j d, let $ = ($; j) be the vector formed by the eigenvalues of the Casimir operators of the d factors of G on V$, and for each p 2 P, we take $;p 0 so that 2 $;p N(p) is the eigenvalue on V$ of the Hecke operator T(p2) For each family of expanding boxes t 7! t , as in (3) in Rd, and fixed an interval Jp in [0;1), for each p 2 P, we consider the counting function N( t; (Jp)p2P) := X $; $2 t : $;p2Jp ;8p2P jcr($)j2 : Here cr($) denotes the normalized Fourier coecient of order r at 1 for the elements of V$, with r 2 O0 F r pO0 F for every p 2 P. In the main result in this paper, Theorem 1.1, we give, under some mild conditions on the t , the asymptotic distribution of the function N( t; (Jp)p2P), as t ! 1. We show that at the finite places outside I the Hecke eigenvalues are equidistributed with respect to the Sato-Tate measure, whereas at the archimedean places the eigenvalues $ are equidistributed with respect to the Plancherel measure. As a consequence, if we fix an infinite place l and we prescribe $; j 2 j for all infinite places j , l and$;p 2 Jp for all finite places p in P (for fixed intervals j and Jp) and then allow j$;lj to grow to 1, then there are infinitely many such $, and their positive density is as described in Theorem 1.1.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
International Press Boston  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
Automorphic Representations  
dc.subject
Hecke Operators  
dc.subject
Hilbert Modular Group  
dc.subject
Plancherel Measure  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Eigenvalues of Hecke operators on Hilbert modular groups  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2016-11-25T14:00:40Z  
dc.journal.volume
17  
dc.journal.number
4  
dc.journal.pagination
729-757  
dc.journal.pais
Estados Unidos  
dc.description.fil
Fil: Bruggeman, Roelof W.. Utrecht University; Países Bajos  
dc.description.fil
Fil: Miatello, Roberto Jorge. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina  
dc.journal.title
Asian Journal of Mathematics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0017/0004/a010/index.html  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4310/AJM.2013.v17.n4.a10  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0912.1692