The Invariant Trace Formula. Ii. Global Theory

The Invariant Trace Formula . 11 . Global Theory

The purpose of this article is to prove an explicit invariant trace formula. In the preceding paper [l(j)] , we studied two families of invariant distributions. Now we shall exhibit these distributions as terms on the two sides of the invariant trace formula. We refer the reader to the introduction of [1 (j)], which contains a general discussion of the problem. In this introduction, we shall de...

Continuous symmetry reduced trace formulas

Trace formulas relate short time dynamics (unstable periodic orbits) to long time invariant state space densities (natural measure). Higher dimensional dynamics requires inclusion of higherdimensional compact invariant sets, such as partially hyperbolic invariant tori, into trace formulas. A trace formula for a partially hyperbolic (N +1)-dimensional compact manifold invariant under a global co...

A stable trace formula III

Introduction This paper is the last of three articles designed to stabilize the trace formula. Our goal is to stabilize the global trace formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases. In the first article [I], we laid out the foundations of the process. We also stated a series of local and global theorems, ...

Trace Formula in Noncommutative Geometry andthe Zeros of the Riemann

We give a spectral interpretation of the critical zeros of the Rie-mann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace formula and eliminates...

The Invariant Trace Formula. I. Local Theory