On geometric density of Hecke eigenvalues for certain cusp forms
type: Item
instance of: scholarly article
title: On geometric density of Hecke eigenvalues for certain cusp forms
zbMATH Open document ID: 1270.11052
author: Goran Muić
published in: Mathematische Annalen
publication date: 2010-04-23T00:00:00Z
review text: Construction of cusp forms is an important problem in the theory of automorphic forms. This paper continues the author's study of the construction of cuspidal automorphic forms via Poincaré series. \textit{G. Muić} [Math. Ann. 343, No. 1, 207--227 (2009; Zbl 1185.11037)]; [Compos. Math. 146, No. 1, 1--20 (2010; Zbl 1248.11038)]; [J. Lie Theory 18, No. 4, 937--949 (2008; Zbl 1163.22005)]; [Ramanujan J. 21, No. 2, 223--239 (2010; Zbl 1237.11023)]; [Proc. Am. Math. Soc. 138, No. 9, 3147--3158 (2010; Zbl 1208.11069)]; [Int. J. Number Theory 7, No. 2, 351--370 (2011; Zbl 1267.11039)]; [J. Number Theory 130, No. 7, 1488--1511 (2010; Zbl 1206.11053)]. Work of other authors dealing with the method of Poincaré series includes \textit{W. L. Baily jun.} and \textit{A. Borel} [Ann. Math. (2) 84, 442--528 (1966; Zbl 0154.08602)], \textit{A. Borel} [Publ. Math., Inst. Hautes Étud. Sci. 16, 101--126 (1963; Zbl 0135.08902)], [Automorphic forms on \(\mathrm{SL}_2(\mathbb R)\). Cambridge: Cambridge University Press (2008; Zbl 1142.11035)], and work discussing other approaches to the problem includes [\textit{J. Arthur},n Clay Math. Proc. 4, 1--263 (2005; Zbl 1152.11021)], [\textit{D. Goldfeld}, Automorphic forms and \(L\)-functions for the group \(\text{GL}(n,\mathbb R)\). Cambridge: Cambridge University Press (2006; Zbl 1108.11039)], [\textit{E. Lindenstrauss} and \textit{A. Venkatesh}, Geom. Funct. Anal. 17, No. 1, 220--251 (2007; Zbl 1137.22011)], [\textit{W. Müller}, Groups and analysis. The legacy of Hermann Weyl. Lond. Math. Soc. Lect. Note Ser. 354, 133--163 (2008; Zbl 1230.11067)], [\textit{T. Miyake}, Modular forms. Berlin: Springer (2006; Zbl 1159.11014)], [\textit{A. Selberg}, J. Indian Math. Soc., N. Ser. 20, 47--87 (1956; Zbl 0072.08201)]. In this paper, the author takes up the study of the Hecke module structure of the space of cusp forms constructed via his refinement of the Poincaré series method. Let \(G\) be a semisimple algebraic group defined over a number field \…
Mathematics Subject Classification ID: 11F60
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 32N10
zbMATH DE Number: 5700562
zbMATH Keywords: Poincare series
zbMATH Keywords: cuspform
zbMATH Keywords: cusp form
zbMATH Keywords: simple trace formula
zbMATH Keywords: Hecke eigenvalue distribution
reviewed by: Joseph Hundley
describes a project that uses: GL(n)pack
MaRDI profile type: Publication
full work available at URL: s00208-009-0444-3
OpenAlex ID: W2013548473
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cites work: On a construction of certain classes of cuspidal automorphic forms via Poincaré series
cites work: Spectral decomposition of compactly supported Poincaré series and existence of cusp forms
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cites work: Q3019014
cites work: Geometry of dual spaces of reductive groups (non-Archimedean case)
DOI: 10.1007/S00208-009-0444-3
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description: scientific article; zbMATH DE number 5700562