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2
votes
1answer
152 views
What is the logarithmic derivative of an (intertwining) operator?
The constant term of the Eisenstein series (for an adele group $GL_2$, say) contains an intertwining operator, often written as $M(s)$. In the form given in Gelbart-Jacquet's Corvallis paper, for ...
11
votes
0answers
493 views
What is the Twisted Trace Formula?
I am studying the trace formula using "An Introduction to the Trace Formula" by James Arthur. I would like to understand the twisted trace formula, but unfortunately I never came across a good ...
0
votes
0answers
23 views
linearization method in smooth transfer of relative trace formula
I'm currently reading Jacquet's paper 'smooth transfer of Kloosterman integrals', in which Jacquet proved there is a smooth transfer for compactly supported smooth functions on GL(n,F) to smooth ...
0
votes
0answers
52 views
stablization of cuspidal terms
Kottwitz, building on the work of Langlands and Shelstad, gave a stabilization of the elliptic terms on the geometric side of the trace formula. This stabilization depended on the endoscopic transfer ...
3
votes
1answer
169 views
Spectral synthesis for central functions on locally compact groups
There is a large literature on harmonic analysis on locally compact group, that
I am just beginning to discover. However I have not seen so far anything that emphasizes the central functions on $G$. A ...
7
votes
1answer
312 views
Trace Class Functions on locally compact groups
Let $G$ be a locally compact subgroup, $\mu$ a Haar-measure.
For $f \in L^1(G)$, and for $\pi$ a unitary, topology irreducible, representation of $G$ on
an Hilbert space $H_\pi$, it is customary to ...
2
votes
1answer
210 views
Arthur-Clozel Prop 3.1 for Function Fields?
The subject says it all. I would like to know if Proposition 3.1 in
Arthur-Clozel's book on the trace formula holds for local fields of positive
characteristic.
Thanks!
EDIT: Here is Prop 3.1 of ...
4
votes
2answers
261 views
vanishing of spectral term in Arthur-Selberg trace formula for GL(2)?
Hi,
In the Arthur-Selberg trace formula for $G = GL(2)/\mathbf Q$ (as seen for example in
Gelbart's "Lectures on the Trace Formula"), the spectral side includes terms
like:
$$
\int_{-\infty}^\infty ...
1
vote
0answers
232 views
on the fundamental lemma
I consider the fundamental lemma for the spherical Hecke algebra.
Let $G$ a connected reductive quasisplit group on $F$, a local field of equal characteristic $p$.
and $H$ an endoscopic group.
Can ...
6
votes
1answer
194 views
Trace formula for PSDOs
In Getzler's famous paper "Pseudodifferential Operators on Supermanifolds and the Atiyah-Singer Index Theorem", he states that for a (trace-class) pseudo-differential operator $P$ on a Riemannian ...
5
votes
0answers
133 views
On Langlands Pairing and transfer factors
In the paper "On the definition of transfer factors" Langlands and Shelstad define a certain number of factors $\Delta_{I}$, $\Delta_{II}$,$\Delta_{III,1}$,$\Delta_{III,2}$, which are roots of unity.
...
8
votes
1answer
782 views
Is this a subcase of the fundamental lemma?
Let $F$ be a local field and $G= GL(n,F)$.
Assume that $\gamma$ is an element of $G$ and $G_\gamma$ is its centralizer.
The orbital integral is defined as
$$ O_\gamma^G( \phi) = ...
4
votes
0answers
504 views
base change and Langlands' combinatorial exercise
Hi,
Is it correct that Langlands' combinatorial exercise (as he terms it in his paper
"Shimura varieties and the Selberg trace formula") is to establish base change identities between orbital ...
9
votes
1answer
830 views
Carayol via the trace formula
Hi,
Is there a proof of the result that Carayol proves in "Sur les representations l-adiques..."
using the Langlands-Kottwitz method of comparing the Lefschetz trace formula and the Selberg trace ...
17
votes
0answers
763 views
Is there a Grothendieck-Riemann-Roch type of theorem generalizing Grothendieck's Lefschetz trace formula
Grothendieck deduced that the L-function of a (constructible) $\ell$-adic sheaf on a variety over $\mathbf{F}_p$ is rational from the generalized trace formula.
My first question is based on the ...
14
votes
0answers
624 views
Computation of low weight Siegel modular forms
We have these huge tables of elliptic curves, which were generated by computing modular forms of weight 2 and level Gamma_0(N) as N increased.
For abelian surfaces over $\mathbf{Q}$ we have very ...
