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 …

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 …

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 $H_\pi$, …

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: Her …

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: $$ \in …

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 $P$ …

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 endo …

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 …

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) = …

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 t …

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 bet …

I'm looking for a formula. in plotting format: x = y to be run through a ranged for loop and plotted. the curve starts as a normal bell curve, and become steeper/sharper progre …

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 …

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 …