Related papers: The twisted symmetric square $L$-function of $GL(r…

We study the behaviour of automorphic L-Invariants associated to cuspidal representations of GL(2) of cohomological weight 0 under abelian base change and Jacquet-Langlands lifts to totally definite quaternion algebras. Under a standard…

We compute by a purely local method the (elliptic) twisted by transpose-inverse character \chi_{\pi_Y} of the representation \pi_Y=I_{(3,1)}(1_3x\chi_Y) of G=GL(4,F), where F is a p-adic field, p not 2, and Y is an unramified quadratic…

We prove algebraicity of critical values of certain Spin $L$-functions. More precisely, our results concern $L(s, \pi \otimes \chi, Spin)$ for cuspidal automorphic representations $\pi$ associated to a holomorphic Siegel eigenform on…

We compute by a purely local method the elliptic, twisted by transpose-inverse, character \chi_\pi of the representation \pi=I_{(3,1)}(1_3) of PGL(4,F) normalizedly induced from the trivial representation of the maximal parabolic subgroup…

We prove an asymptotic formula for the second moment of the $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ Rankin--Selberg central $L$-values $L(1/2,\Pi\otimes\pi)$, where $\pi$ is a fixed cuspidal representation of $\mathrm{GL}(n)$ that is…

Let \pi be a cuspidal automorphic representation of GL_4 with central character \mu^2. It is known that \pi has Shalika period with respect to \mu if and only if the L-function L^S(s, \pi, \bigwedge^2\otimes\mu^{-1}) has a pole at s=1.…

Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime. In this note we revisit the subconvexity problem addressed in `The circle method and bounds…

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…

Let $\pi$ traverse a sequence of cuspidal automorphic representations of GL(2) with large prime level, unramified central character and bounded infinity type. For G either of the groups GL(1) or PGL(2), let H(G) denote the assertion that…

We show that the Gelfand character $ \chi_G$ of a finite group $G $ (i.e. the sum of all irreducible complex characters of $G$ ) may be realized as a `` twisted trace'' $ g \mapsto Tr( \rho_g \circ T) $ for a suitable involutive linear…

In this work we develop an integral representation for the partial $L$-function of a pair $\pi\times\tau$ of genuine irreducible cuspidal automorphic representations, $\pi$ of the $m$-fold covering of Matsumoto of the symplectic group…

We give a Burgess-like subconvex bound for $L(s, \pi \otimes \chi)$ in terms of the analytical conductor of $\chi$, where $\pi$ is a $GL_2$ cuspidal representation and $\chi$ is a Hecke character.

Let $\pi$ be an irreducible unitary cuspidal representation for $GL_m({\Bbb A}_{\Bbb Q})$, and let $L(s, \pi)$ be the automorphic $L$-function attached to $\pi$, which has a Dirichlet series expression in the half-plane $\mbox{Re} s>1$.…

We prove a Burgess-like subconvex bound for twisted L-functions of a fixed irreducible cuspidal automorphic representation of GL(2) over a totally real number field. The proof is based on a spectral decomposition of shifted convolution sums…

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid subconvex…

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…

Let $F/k$ be a cyclic extension of number fields of prime degree. Let $\rho$ be an irreducible $2$-dimensional representation of Artin type of the absolute Galois group of $F$, and $\pi$ a cuspidal automorphic representation of…

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…

For $m\ge 2$, let $\pi$ be an irreducible cuspidal automorphic representation of $GL_m(\mathbb{A}_{\mathbb{Q}})$ with unitary central character. Let $a_\pi(n)$ be the $n^{th}$ coefficient of the $L$-function attached to $\pi$. Goldfeld and…

Let $K$ be a quadratic imaginary field. Let $\Pi$ (resp. $\Pi'$) be a regular algebraic cuspidal representation of $GL_{n}(K)$ (resp. $GL_{n-1}(K)$) which is moreover cohomological and conjugate self-dual. In \cite{harris97}, M. Harris has…