Abstract

In this paper we develop the local theory for a Jacquet's relative trace formula. The local theory is essential to the application of the trace formula: it is an identity of Bessel and relative Bessel distributions. We show that the relative Bessel distribution attached to a distinguished (that is, self contragradient) unitary representation of GL2(k) where k is a p-adic field is given by a locally integrable function, namely the relative Bessel function. We compute the relative Bessel function for principal series, complementary series and special representations. We also show that the Bessel distributions associated to unitary irreducible admissible representations of the double covers of GL2(k) and SL2(k) are given by a locally integrable Bessel functions. We compute these Bessel functions for principal series, complementary series and special representations. Finally, we obtain the Waldspurger correspondence via Bessel identities between relative Bessel functions on GL2(k) and Bessel functions on the double cover of SL2(k). The Bessel identity also implies the identity between Bessel and relative Bessel distributions.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 225-288
Launched on MUSE
2003-03-26
Open Access
No
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