Author | Rallis, Stephen. author |
---|---|

Title | L-Functions and the Oscillator Representation [electronic resource] / by Stephen Rallis |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1987 |

Connect to | http://dx.doi.org/10.1007/BFb0077894 |

Descript | XVI, 240 p. online resource |

SUMMARY

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

CONTENT

Notation and preliminaries -- Special Eisenstein series on orthogonal groups -- Siegel formula revisited -- Inner product formulae -- Siegel formula โ{128}{148} Compact case -- Local l-factors -- Global theory

Mathematics
Number theory
Mathematics
Number Theory