Side cut method of examining trace component.

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...

8. Component Architectures 8.1 Software Components 8.2 Client-side Component Architecture 8.3 Foundation for Server-side Component Architecture 8.4 Server-side Component Architecture

On the Spectral Side of Arthur’s Trace Formula Ii

We derive a refinement of the spectral expansion of Arthur’s trace formula. The expression is absolutely convergent with respect to the trace norm.

The Short-Cut Metropolis Method

I show how one can modify the random-walk Metropolis MCMC method in such a way that a sequence of modified Metropolis updates takes little computation time when the rejection rate is outside a desired interval. This allows one to effectively adapt the scale of the Metropolis proposal distribution, by performing several such “short-cut” Metropolis sequences with varying proposal stepsizes. Unlik...

On the spectral side of Arthur’s trace formula — absolute convergence

We derive a refinement of the spectral expansion of Arthur’s trace formula. The expression is absolutely convergent with respect to the trace norm.