Vol. 260, No. 2, 2012

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A relative trace formula for PGL(2) in the local setting

Brooke Feigon

Vol. 260 (2012), No. 2, 395–432

We develop the local Kuznetsov trace formula on a unitary group in two variables for an unramified quadratic extension of local, non-Archimedean fields E∕F and compare it to a local relative trace formula on PGL(2,E). To define the local distributions for the relative trace formula, we define a regularized local period integral and prove that it is a PGL(2,F)-invariant linear functional. By comparison of the two local trace formulas, we get an equality between a local PGL(2,F)-period and local Whittaker functionals.

relative trace formula
Mathematical Subject Classification 2010
Primary: 11F70, 22E50
Received: 19 July 2012
Revised: 9 October 2012
Accepted: 16 October 2012
Published: 30 November 2012
Brooke Feigon
Department of Mathematics
The City College of New York, CUNY
NAC 8/133
New York, NY 10031
United States