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Results tagged with trace-formula
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user 10400
Theoretical issues and applications of the Selberg, Arthur and relative trace formulas
2
votes
Regularity assumption in the simple trace formula
If you don't make that assumption, you also will get "one-dimensional" representations. For example, consider $G=GL(2)$ and $F$ global function field, assume at two place pseudo matrix coefficient for …
- 11.2k
3
votes
Accepted
Arthur-Clozel Prop 3.1 for Function Fields?
This can be found in Laumon Cohomology of Drinfeld modules fourth chapter.
- 11.2k
1
vote
Accepted
What is the logarithmic derivative of an (intertwining) operator?
The functional equation gives $M(s)M(-s)=1$, so yes $M(-s)=M^{-1}(s)$. Note that $M(s)'$ is not an intertwiner, only intertwines the compact group $K$ in $GL_2(A)$. The irreducible $K$-isotypes of $GL …
- 11.2k
2
votes
Accepted
vanishing of spectral term in Arthur-Selberg trace formula for GL(2)?
Sorry, my original answer was adressing vanishing of the contribution of the continuous spectrum. You are asking for something different.
If the $\infty$ component is a pseudo coefficient of the disc …
- 11.2k
5
votes
Accepted
Trace Class Functions on locally compact groups
The following is a suggestion how to prove a weak variant of the OP's original question affirmative.
Theorem: Let $G$ be a unimodular, seperable, type-I group.
For every element $\phi$ in $C_c^\ …
- 11.2k
2
votes
Accepted
Spectral synthesis for central functions on locally compact groups
This a long comment, which indicates the difficulties and gives a decomposition of measures in terms of orbital integrals instead of irreducible reps.
As you have noticed yourself, there do not exist …
- 11.2k