Related papers: Integral Representaion for L-functions for GSp(4)x…

For a non-endoscopic cohomological cuspidal automorphic representation of $\mathrm{GSp}_4 \times \mathrm{GL}_2$, assumed to be $p$-ordinary, we construct an Euler system for the Galois representation associated to it. Both the construction…

We show the existence of an L-functions of a cuspidal representation of GSp(4,A)*GSp(4,A) which has a pole of order 2 at s = 1, even for globally generic representations. However if \pi comes from GSO(4,A), then \pi? is the Weil transfer of…

We construct an Euler system for Galois representations associated to cohomological cuspidal automorphic representations of the group GSp(4), using the pushforwards of Eisenstein classes for GL(2) x GL(2).

We construct an integral representation for the global Rankin-Selberg (partial) $L$-function $L(s, \pi \times \tau)$ where $\pi$ is an irreducible globally generic cuspidal automorphic representation of a general spin group (over an…

For a cuspidal automorphic representation \Pi of GL(4,A), H. Kim proved that the exterior square transfer \wedge^2\Pi is an isobaric automorphic representation of GL(6,A). In this paper we characterize those representations \Pi for which…

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…

We provide a definition for an extended system of $\gamma$-factors for products of generic representations $\tau$ and $\pi$ of split classical groups or general linear groups over a non-archimedean local field of characteristic $p$. We…

We establish the existence of congruences between a fixed endoscopic cuspidal automorphic representation $\Pi$ of $\mathrm{GSp}(4)$ of square-free conductor and stable cuspidal automorphic representations of the same level and weight modulo…

For integers $m, m' \ge 1$, let $\pi$ and $\pi'$ be cuspidal automorphic representations of $\mathrm{GL}(m)$ and $\mathrm{GL}(m')$, respectively. We present a new proof of zero-free regions for $L(s, \pi)$ and for $L(s, \pi \times \pi')$…

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…

A family of global integrals representing a product of tensor product (partial) $L$-functions: $ L^S(s,\pi\times\tau_1)L^S(s,\pi\times\tau_2)... L^S(s,\pi\times\tau_r) $ are established in this paper, where $\pi$ is an irreducible cuspidal…

Given a cuspidal Hilbert modular eigenform $\pi$ of parallel weight 2 and a nonarchimedian place $\mathfrak p$ of the underlying totally real field such that the local component of $\pi$ at $\mathfrak p$ is the Steinberg representation, one…

Let $\mathcal{L}^{S}\left(s,\pi,\chi,\operatorname{\mathfrak{st}}\right)$ be a standard twisted partial $\mathcal{L}$-function of degree $7$ of the cuspidal automorphic representation $\pi$ of the exceptional group of type $G_2$. In this…

Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue characteristic p and G be an inner form of GL(2n,F). This is a group of the form GL(r,D) for a positive integer r and division F-algebra D of reduced…

We use modular symbols to construct p-adic L-functions for cohomological cuspidal automorphic representations on GL(2n), which admit a Shalika model. Our construction differs from former ones in that it systematically makes use of the…

We construct four-variable $p$-adic $L$-functions for the spin Galois representation of a Siegel modular form of genus 2 twisted by the Galois representation of a cuspidal modular form as the modular forms vary in Coleman families. The main…

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…

In this paper we explicitly compute mod-l Galois representations associated to modular forms. To be precise, we look at cases with l<=23 and the modular forms considered will be cusp forms of level 1 and weight up to 22. We present the…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$, and let $\sigma$ denote its non-trivial automorphism. Let $R$ be an algebraically closed field of characteristic different…

We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups…