2,240 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
The Manifestation of Stress and Rumination in Musicians
Here we offer a brief review of research on individual differences that are common to musicians, focusing on our own work on rumination and stress. Rumination and stress have been linked with depression and negative health outcomes. We discuss two of our published studies and two new, unpublished replications that find elevated levels of rumination and stress in musicians. Further, we review literature that finds this combination of rumination and stress might be especially toxic. Even though people frequently use music to help combat stress, musicians may not be taking advantage of their frequent exposure to music, further exacerbating the problem. Interventions aimed at alleviating stress and rumination might prove helpful to musicians
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