A Local Relative Trace Formula for F*(2,F)
Abstract
In this note, we derive explicitly the local relative trace formula for the symmetric space F*(2,F) at the level of Lie algebras, where F is a p-adic field of residue characteristic greater than two and F* is the set of invertible elements in F. This is perhaps one of the simplest non-trivial analogs of the trace formula, and also a motivating example for the author's work (in preparation) on the relative trace formula.
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