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Results tagged with trace-formula
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user 6518
Theoretical issues and applications of the Selberg, Arthur and relative trace formulas
1
vote
Regularity assumption in the simple trace formula
Probably the OP has figured this out by now, but for posterity let me explain (in the general setting of simple trace formulas, rather than the specific Deligne-Kazhdan case):
A trace formula $I(f) = …
- 6,039
3
votes
Selberg trace formula, quadratic L-values, and generalization
If I understand correctly what you are looking for, then yes, a fair amount of work has been done. Deitmar and Hoffman use a simple trace formula on SL(3) to get asymptotics of class number of cubic …
- 6,039
4
votes
Accepted
A trace formula for $\mathrm{GSp(4)}$
There are many kinds of trace formulas on a given group $G$, and different things you could mean by decomposition of the spectrum. As mentioned in the comments, there's Arthur's article in the Shalik …
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5
votes
Arthur's Simple Trace Formula
Yes, I have not known Deligne, Kazhdan and Vigneras to lie. A sketch of the proof, at least with the key details for GL(2), is given in Lecture V of
Steve Gelbart, Lectures on the Arthur--Selberg Tr …
- 6,039
5
votes
Comparing Selberg and Eichler-Selberg trace formulas
Trace formulas, and in particular the Selberg trace formula, is an identity $I(f) = J(f)$ of spectral and global distributions where $f$ is a test function. There are different ways to use the trace …
- 6,039
9
votes
Accepted
Reaching Hecke eigenvalues from a trace formula
Yes, this is a standard thing to do. If you want to look at traces of Hecke operators on a definite quaternion algebra, this is the same as what are known as "traces of Brandt matrices." These have …
- 6,039
23
votes
Accepted
What is the status of Arthur's book?
Updated answer (Oct 2024):
While Arthur did not finish some preprints referred to in his book ([A24]-[A27]), [A24] was dealt with by Moeglin and Waldspurger, and this arXiv preprint which was just pos …
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