17 research outputs found
Invariant four-variable automorphic kernel functions
Let be a number field, let be its ring of adeles, and let
. Previously the author
provided an absolutely convergent geometric expression for the four variable
kernel function where the sum is over isomorphism classes of cuspidal
automorphic representations of . Here
is the typical kernel function representing the action of a test
function on the space of the cuspidal automorphic representation . In this
paper we show how to use ideas from the circle method to provide an alternate
expansion for the four variable kernel function that is visibly invariant under
the natural action of .Comment: The formula in this version is more explicit and simpler than the
previous versio
A nonabelian trace formula
Let be an extension of number fields with simple
and nonabelian. In [G] the first named author suggested an approach to
nonsolvable base change and descent of automorphic representations of
along such an extension. Motivated by this we prove a trace
formula whose spectral side is a weighted sum over cuspidal automorphic
representations of that are isomorphic to their
-conjugates.Comment: Comments are welcom