Related papers: Poles of triple product $L$-functions involving mo…

Let $\pi=\pi_1 \otimes \pi_2 \otimes \pi_3$ be a unitary cuspidal automorphic representation of $\mathrm{GL}_3^3(\mathbb{A}_F)$ where $F$ is a number field. Assume that $\pi$ is everywhere tempered. Under suitable local hypotheses, for a…

Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. We study these problems in a setting related to the Langlands $L$-functions…

Motivated by the Langlands' beyond endoscopy proposal for establishing functoriality, we study the representation $\otimes^3$ in a setting related to the Langlands $L$-functions $L(s,\pi,\,\otimes^3),$ where $\pi$ is a cuspidal automorphic…

Let $F$ be a number field. Let $\pi_1,\pi_2$ be cuspidal automorphic representations of $GL_2(\mathbb{A}_F)$, and let $\pi$ be a cuspidal automorphic representation of either $GL_2(\mathbb{A}_F)$ or $GL_3(\mathbb{A}_F)$. When…

Let $\pi_1, \pi_2, \pi_3$ be three cuspidal automorphic representations for the group ${\rm SL}(2, \Bbb{Z})$, where $\pi_1$ and $\pi_2$ are fixed and $\pi_3$ has large conductor. We prove a subconvex bound for $L(1/2, \pi_1 \otimes \pi_2…

In this paper we prove a conjecture of Ginzburg and Soudry on an integral representation for the $L$-function $L^S(s, \pi\times \tau)$ attached to a pair $(\pi, \tau)$ of irreducible automorphic cuspidal representations of…

We present an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical…

Let $M=GL_{r_1}\times\cdots\times GL_{r_k}\subseteq GL_r$ be a Levi subgroup of $GL_r$, where $r=r_1+\cdots+r_k$, and $\tilde{M}$ its metaplectic preimage in the metaplectic cover $\tilde{GL}_r$ of $GL_r$. For automorphic representations…

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…

We study the restriction of the Bump-Friedberg integrals to affine lines $\{(s+\alpha,2s),s\in\C\}$. It has a simple theory, very close to that of the Asai $L$-function. It is an integral representation of the product…

We prove a prime number theorem first for the classical Rankin-Selberg L-function $L(s,\pi\times\pi')$ over any Galois extension with $\pi$ and $\pi'$ unitary automorphic cuspidal representations of $GL_n$ and $GL_m$ respectively with at…

Let $\pi$ be a square integrable representation of a classical group and let $\rho$ be a cuspidal representation of a general linear group. We can define in two different ways an L-function $L(\rho \times \pi,s)$: first we can use the…

In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\rm GL}_6\times {\rm GL}_1$ to that of the quasi-split unitary similitude group ${\rm GU}_6$ and establish its analytic…

Given unitary automorphic cuspidal representations $\pi$ and $\pi'$ defined on $GL_n(\mathbb{A}_E)$ and $GL_m(\mathbb{A}_F)$, respectively, with $E$ and $F$ solvable algebraic number fields we deduce a prime number theorem for the…

Let $E/F$ be a quadratic extension of non-archimedean local fields, and let $\ell$ be a prime number different from the residual characteristic of $F$. For a complex cuspidal representation $\pi$ of $GL(n,E)$, the Asai $L$-factor…

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…

We consider a new integral representation for $L(s_1, \Pi \times \tau_1) L(s_2, \Pi \times \tau_2),$ where $\Pi$ is a globally generic cuspidal representation of $GSp_4,$ and $\tau_1$ and $\tau_2$ are two cuspidal representations of $GL_2$…

Based on Furusawa's theory, we present an integral representation for the L-function L(s,\pi \times \tau), where \pi is a cuspidal automorphic representation on GSp(4) related to a holomorphic Siegel modular form, and where \tau is an…

Let $F$ be a number field with adele ring $\mathbb{A}_F$, $\pi_1, \pi_2$ be two unitary cuspidal automorphic representations of $\mathrm{PGL}_2(\mathbb{A}_F)$ with finite analytic conductor. We study the twisted first moment of the triple…

We prove three main results: all Langlands-Shahidi automorphic $L$-functions over function fields are rational; after twists by highly ramified characters our automorphic $L$-functions become polynomials; and, if $\pi$ is a globally generic…