Hello, I have the following problem : Let $(G,G')$ and $(H,H')$ be a pair of dual reductive pairs in a symplectic space $Sp(W)$ (in a global setting) forming a seesaw pair (with $ …

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 …

The definition I know of for a cuspidal automorphic representation of, say, $G=\mathrm{GL}_2$ over a number field $F$ (relative to a choice of compact open subgroup $K_f$ of $G(\ma …

Hello. I have some question on Cartan decomposition of unitary group, especially $U(2)$. I am interested in local situation, that is p-adic or archimedian. Let $F$ be a local fie …

Some colleagues and I were wondering if there is a citation out there which shows there are no exceptional eigenvalues, $\lambda$, of classical weight 1/2 Maass forms on $\Gamma_0( …

I am trying to read Harish-Chandra's book on automorphic forms on Semisimple Lie groups, and he keeps referring to Borel's Paris lecture notes. Does anyone have an online version o …

Let $F_v$ be a local field. Let $\sigma_v$ be a two-dimensional representation of $Gal(\overline{F}_v:F_v) \rtimes W_{F_v}$. Now, there exists an infinite-dimensional representatio …

Shimura lifts are correspondence between integer weight and half-integral weight automorphic forms. Half integral weight things are associated to representation of a double cover o …

I have a question about the terminology for special values of L-functions. Is the following a correct description of standard usage: Suppose L(s) is an L-function which satisfies …

The MSRI is organising a programme with the above title from Aug 11, 2014 to Dec 12, 2014. Here is a short description from their website : The branches of number theory most …

Though I am in a situation considering only local-zeta integral, to explain my question briefly, let me ask it in quite general form. Let $f(s,g)$ be a two variable smooth good (i …

This is more of a question about terminology than about math. The term "automorphic form" is clearly a generalization of the term "modular form." What is not clear is exactly whic …

Let $G$ be an algebraic group over a field $F$. Let $g\in G(F)$, and write $C(g)$ for the centralizer of $g$ in $G$. Conjugacy over $F$ is of course not necessarily the same thing …

Let $f(z) = \sum_{n=1}^\infty A(n)n^{\frac{k-1}{2}}e(nz)$ be a modular form of weight $k$ for a half integer $k$. Put $$L(s,f) = \sum_{n=1}^\infty \frac{A(n)}{n^s} $$ to be the $L$ …

How does one prove that an Eisenstein series (adelically formulated as in the book of Moeglin-Waldspurger) is not identically zero? Namely how does one prove that the sum $\sum_{\g …