By Stephen Rallis

Those notes are interested by exhibiting the relation among L-functions of classical teams (*F1 particularly) and *F2 features bobbing up from the oscillator illustration of the twin reductive pair *F1 *F3 O(Q). the matter of measuring the nonvanishing of a *F2 correspondence by way of computing the Petersson internal fabricated from a *F2 carry from *F1 to O(Q) is taken into account. This product may be expressed because the distinctive price of an L-function (associated to the normal illustration of the L-group of *F1) instances a finite variety of neighborhood Euler elements (measuring no matter if a given neighborhood illustration happens in a given oscillator representation). the most important rules utilized in proving this are (i) new Rankin essential representations of normal L-functions, (ii) see-saw twin reductive pairs and (iii) Siegel-Weil formulation. The e-book addresses readers who concentrate on the idea of automorphic varieties and L-functions and the illustration conception of Lie teams. N

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