L-Functions and the Oscillator Representation
Seiten
1987
|
1987
Springer Berlin (Verlag)
978-3-540-17694-7 (ISBN)
Springer Berlin (Verlag)
978-3-540-17694-7 (ISBN)
These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N
Notation and preliminaries.- Special Eisenstein series on orthogonal groups.- Siegel formula revisited.- Inner product formulae.- Siegel formula - Compact case.- Local l-factors.- Global theory.
Erscheint lt. Verlag | 25.3.1987 |
---|---|
Reihe/Serie | Lecture Notes in Mathematics |
Zusatzinfo | XVI, 240 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 363 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | automorphic forms • Lie group • Representation Theory |
ISBN-10 | 3-540-17694-2 / 3540176942 |
ISBN-13 | 978-3-540-17694-7 / 9783540176947 |
Zustand | Neuware |
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