Related papers: A cuspidality criterion for the functorial product…

We prove the existence of a cuspidal automorphic representation $\pi$ for $GL_{79}/\mathbf{Q}$ of level one and weight zero. We construct $\pi$ using symmetric power functoriality and a change of weight theorem, using Galois deformation…

In a previous paper [3] we computed cohomology groups H^5 (Gamma_0 (N), \C), where Gamma_0 (N) is a certain congruence subgroup of SL (4, \Z), for a range of levels N. In this note we update this earlier work by extending the range of…

In this article, we establish an asymptotic lower bound estimate on the contribution of cuspidal automorphic representations of ${\rm GL}_4(\mathbb A_{\mathbb Q})$ to cuspidal cohomology of the ${\rm GL}_4$ which are obtained from…

We define a new notion of cuspidality for representations of $\GL_n$ over a finite quotient $\Oh_k$ of the ring of integers $\Oh$ of a non-Archimedean local field $F$ using geometric and infinitesimal induction functors, which involve…

We extend the work of Ash and Stevens [Ash-Stevens 97] on p-adic analytic families of p-ordinary arithmetic cohomology classes for GL(N,Q) by introducing and investigating the concept of p-adic rigidity of arithmetic Hecke eigenclasses. An…

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having…

In this article, we are concerned with the Langlands functoriality conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality conjecture in the case of a globally generic cuspidal automorphic representation for the split…

Fix $n \geq 2$ an integer, and let $F$ be a totally real number field. We derive estimates for the finite parts of the $L$-functions of irreducible cuspidal $\operatorname{GL}_n({\bf{A}}_F)$-automorphic representations twisted by class…

In this paper we prove two new cases of Langlands functoriality. The first is a functorial product for cusp forms on $GL_2\times GL_3$ as automorphic forms on $GL_6$, from which we obtain our second case, the long awaited functorial…

Let $\pi$ be a unitary automorphic cuspidal representation of $GL_2(\mathbb{Q}_\mathbb{A})$ with Fourier coefficients $\lambda_\pi(n)$. Asymptotic expansions of certain sums of $\lambda_\pi(n)$ are proved using known functorial liftings…

Given a cuspidal automorphic representation of GL(2) over a global function field, we establish a comprehensive cuspidality criterion for symmetric powers. The proof is via passage to the Galois side, possible over function fields thanks to…

A systematic analysis is presented of compactifications of the IIB superstring on $AdS_5 \times S^5/\Gamma$ where $\Gamma$ is a non-abelian discrete group. Every possible $\Gamma$ with order $g \leq 31$ is considered. There exist 45 such…

We prove that for any m > 1 given any m-tuple of Hecke eigenforms $f_i$ of level 1 whose weights satisfy the usual regularity condition there is a self-dual cuspidal automorphic form $\pi$ of $\GL_{2^m}(\Q)$ corresponding to their tensor…

The main result of this article proves the nonvanishing of cuspidal cohomology for $GL(n)$ over a number field which is Galois over its maximal totally real subfield. The proof uses the internal structure of a strongly-pure weight that can…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields with residual characteristic $p\neq2$, and $\ell$ be a prime number different from $p$. We classify those $\ell$-modular cuspidal irreducible representations of…

Let $V$ be a M\"{o}bius vertex algebra and $G$ an abelian group of automorphisms of $V$. We construct $P(z)$-tensor product bifunctors for the category of $C_{n}$-cofinite grading-restricted generalized $g$-twisted $V$-modules (without…

If $L(s,\pi)$ and $L(s,\rho)$ are the Dirichlet series attached to cuspidal automorphic representations $\pi$ and $\rho$ of ${\rm GL}_n({\mathbb A}_{\mathbb Q})$ and ${\rm GL}_{n-2}({\mathbb A}_{\mathbb Q})$ respectively, we show that…

Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on GL(1)) was used by Dirichlet to prove…

Modular symbols for the congruence subgroup $\Gamma_0(\mathfrak{n})$ of $GL_{2}(\mathbf{F}_q[T])$ have been defined by Teitelbaum. They have a presentation given by a finite number of generators and relations, in a formalism similar to…

Aimed at geometric applications, we prove the homology cobordism invariance of the $L^2$-betti numbers and $L^2$-signature defects associated to the class of amenable groups lying in Strebel's class $D(R)$, which includes some interesting…