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Asymptotic Expansions for Dirichlet Series Associated to Cusp Forms

  • We prove an asymptotic expansion of Riemann-Siegel type for Dirichlet series associated to cusp forms. Its derivation starts from a new integral formula for the Dirichlet series and uses sharp asymptotic expansions for partial sums of the Fourier series of the cusp form.

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Author:Andreas Guthmann
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7956
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (300)
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Dirichlet series; Riemann-Siegel formula; cusp forms
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):11-XX NUMBER THEORY / 11Mxx Zeta and L-functions: analytic theory / 11M41 Other Dirichlet series and zeta functions (For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72)
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011