Local Orbital Integrals of a Relative Trace Formula

1 Local Orbital Integrals In Ref. [1] Jacquet and Ye conjectured a relative trace formula for GL(n) which could be used to show that an automorphic representation π of GL(n) over a number field is a quadratic base change if and only if it is distinguished, a theorem first proved by Harder, Langlands and Rapoport for GL(2). This property of π being distinguished then might imply a possible pole of an L-function attached to the representation π. For GL(2)