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Local Newforms for GSp(4) [electronic resource] / by Brooks Roberts, Ralf Schmidt.

Por: Roberts, Brooks [author.]Colaborador(es): Schmidt, Ralf [author.]Tipo de material: TextoTextoSeries Lecture Notes in Mathematics, 1918Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Descripción: VIII, 312 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783540733249Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Topological Groups | Number theory | Mathematics | Number Theory | Topological Groups, Lie GroupsFormatos físicos adicionales: Sin títuloClasificación CDD: 512.7 Clasificación LoC:QA241-247.5Recursos en línea: de clik aquí para ver el libro electrónico
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Springer eBooksResumen: Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).
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A Summary -- Representation Theory -- Paramodular Vectors -- Zeta Integrals -- Non-supercuspidal Representations -- Hecke Operators -- Proofs of the Main Theorems.

Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).

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