A local relative trace formula for PGL(2)

Towards a Local Trace Formula

is then a unitary representation of G(F) X G(F) on L2(G(F)). Kazhdan has suggested that there should be a local trace formula attached to R which is analogous to the global trace formula for automorphic forms. The purpose of this note is to discuss how one might go about proving such an identity, and to describe the ultimate form the identity is likely to take. To see the analogy with automorph...

A Local Trace Formula for Anosov Flows

We prove a local trace formula for Anosov flows. It relates Pollicott–Ruelle resonances to the periods of closed orbits. As an application, we show that the counting function for resonances in a sufficiently wide strip cannot have a sublinear growth. In particular, for any Anosov flow there exist strips with infinitely many resonances.

Harmonic analysis for relative trace formula

Many questions on special values of L-functions are tied to the study of period integrals of automorphic forms. A notable example is the formula of Waldspurger ([22]) that relates the toric period on GL2 or its inner form to some central critical L-value. The conjecture of Gan, Gross and Prasad ([4]) started with the Gross-Prasad conjecture ([5]), as well as the refinement of Ichino and Ikeda (...

A Kloosterman Sum in a Relative Trace Formula for Gl4

We study a Kloosterman sum for GL4 and prove that it is equal to an exponential sum over a quadratic number field. This identity has applications in a relative trace formula for GL4 which might be used to give a new proof of quadratic base change and characterize its image.

The Invariant Trace Formula. I. Local Theory