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Orthogonality relations for Poincaré series.

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Title: Orthogonality relations for Poincaré series.
Authors: Žunar, Sonja1 szunar@geof.hr
Source: Mathematical Communications. 2025, Vol. 30 Issue 2, p161-169. 9p.
Subjects: Poincaré series, Automorphic forms, Lie groups, Inner product spaces
Abstract: Let G be a connected semisimple Lie group with finite center. We prove a formula for the inner product of two cuspidal automorphic forms on G that are given by Poincaré series of K-finite matrix coefficients of an integrable discrete series representation of G. As an application, we give a new proof of a well-known result on the Petersson inner product of certain vector-valued Siegel cusp forms. In this way, we extend results previously obtained by Muić for cusp forms on the upper half-plane, i.e., in the case when G = SL2 (R). [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Communications is the property of University of Osijek, Department of Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Orthogonality relations for Poincaré series.
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  Data: <searchLink fieldCode="DE" term="%22Poincaré+series%22">Poincaré series</searchLink><br /><searchLink fieldCode="DE" term="%22Automorphic+forms%22">Automorphic forms</searchLink><br /><searchLink fieldCode="DE" term="%22Lie+groups%22">Lie groups</searchLink><br /><searchLink fieldCode="DE" term="%22Inner+product+spaces%22">Inner product spaces</searchLink>
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  Data: Let G be a connected semisimple Lie group with finite center. We prove a formula for the inner product of two cuspidal automorphic forms on G that are given by Poincaré series of K-finite matrix coefficients of an integrable discrete series representation of G. As an application, we give a new proof of a well-known result on the Petersson inner product of certain vector-valued Siegel cusp forms. In this way, we extend results previously obtained by Muić for cusp forms on the upper half-plane, i.e., in the case when G = SL2 (R). [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Mathematical Communications is the property of University of Osijek, Department of Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.64785/mc.30.2.1
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 161
    Subjects:
      – SubjectFull: Poincaré series
        Type: general
      – SubjectFull: Automorphic forms
        Type: general
      – SubjectFull: Lie groups
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      – SubjectFull: Inner product spaces
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      – TitleFull: Orthogonality relations for Poincaré series.
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            – D: 01
              M: 07
              Text: 2025
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              Y: 2025
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