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    INTEGRAL MOMENTS OF AUTOMORPHIC L�FUNCTIONS

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    Abstract. We obtain second integral moments of automorphic Lfunctions on adele groups GL2 over arbitrary number fields, by a spectral decomposition using the structure and representation theory of adele groups GL1 and GL2. This requires complete reformulation of the notion of Poincar series, replacing the collection of classical Poincar series over GL2(Q) or GL2(Q(i)) with a single, coherent, global object that makes sense over a number field. This is the first expression of integral moments in adele-group-theoretic terms, distinguishing global and local issues, and allowing uniform application to number fields. When specialized to the field of rational numbers Q, we recover the classical results on moments. 1.

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    Title : INTEGRAL MOMENTS OF AUTOMORPHIC L�FUNCTIONS
    Abstract : Abstract. We obtain second integral moments of automorphic Lfunctions on adele groups GL2 over arbitrary number fields, by a spectral decomposition using the structure and representation theory of adele groups GL1 and GL2. This requires complete reformulation of the notion of Poincar series, replacing the collection of classical Poincar series over GL2(Q) or GL2(Q(i)) with a single, coherent, global object that makes sense over a number field. This is the first expression of integral moments in adele-group-theoretic terms, distinguishing global and local issues, and allowing uniform application to number fields. When specialized to the field of rational numbers Q, we recover the classical results on moments. 1.
    Subject : unspecified
    Area : Mathematics
    Language : English
    Affiliations : 
    Url : http://www.math.umn.edu/~garrett/m/v/intmo_05_mar.pdf
    Doi : 10.1.1.115.2109

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