University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Mathematics
    • Mathematics Theses and Dissertations
    • View Item
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Mathematics
    • Mathematics Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    The Metaplectic Case of the Weil-Siegel Formula

    Thumbnail
    View/Open
    1173431.pdf (8.761Mb)
    No. of downloads: 94

    Date
    1990
    Author
    Sweet, William Jay Jr.
    Advisor
    Kudla, Stephen S.
    DRUM DOI
    https://doi.org/10.13016/M27940W22
    Metadata
    Show full item record
    Abstract
    The Weil-Siegel formula, in the form developed by Weil, asserts the equality of a special value of an Eisenstein series with the integral of a related theta series. Recently, Kudla and Rallis have extended the formula into the range in which the Eisenstein series fails to converge at the required special value, so that Langlands' meromorphic analytic continuation must be used. In the case addressed by Kudla and Rallis, both the Eisenstein series and the integral of the theta series are automorphic forms on the adelic symplectic group. This thesis concentrates on extending the Weil-Siegel formula in the case in which both functions are automorphic forms on the two-fold metaplectic cover of the adelic symplectic group. First of all, a concrete model of the global metaplectic cover mentioned above is constructed by modifying the local formulas of Rao. Next, the meromorphic analytic continuation of the Eisenstein series is shown to be holomorphic at the special value in question. In the course of this work, we develop the functional equation and find all poles of an interesting family of local zeta-integrals similar to those studied in a paper of Igusa. Finally, the Weil-Siegel formula is proven in many cases by the methods of Kudla and Rallis.
    URI
    http://hdl.handle.net/1903/20246
    Collections
    • Mathematics Theses and Dissertations
    • UMD Theses and Dissertations

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility