Geometric side of a local relative trace formula

On the Θ-split Side of the Local Relative Trace Formula

The author derives an expression for one side of the local relative trace formula at the level of Lie algebras, by combining methods of Arthur and Harish-Chandra with the structure theory of reductive symmetric spaces.

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...

The spectral side of Arthur's trace formula.

The trace formula is one of the most important tools in the theory of automorphic forms. It was invented in the 1950's by Selberg, who mostly studied the case of hyperbolic surfaces, and was later on developed extensively by Arthur in the generality of an adelic quotient of a reductive group over a number field. Here we provide an explicit expression for the spectral side, improving Arthur's fi...

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.

Geometric Estimates for the Trace Formula