Related papers: Whittaker functions associated to newforms for GL(…

Let G be the unramified unitary group in three variables defined over a p-adic field F of odd resudual characteristic. Gelbart, Piatetski-Shapiro and Baruch attached zeta integrals of Rankin-Selberg type to irreducible generic…

We use the Langlands--Shahidi method in order to define the Shahidi gamma factor for a pair of irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_m\left(\mathbb{F}_q\right)$. We…

Let $\theta$ and $\theta'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $\theta\otimes\theta'$ is a (very large) representation of $GL_n$. We…

In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group $\GL_n(\mathbb F_q)$. Green's theory of $\GL_n(\mathbb F_q)$ is recovered and enhanced under the…

We construct p-adic L-functions associated to cuspidal Hilbert modular eigenforms of parallel weight two in certain dihedral or anticyclotomic extensions via the Jacquet-Langlands correspondence, generalizing works of Bertolini-Darmon,…

Let $F$ be a non archimedean local field of characteristic zero, we give a classification of generic representations of $GL(n,F)$ distinguished by a maximal Levi subgroup, in terms of inducing discrete series.

Let F be a local field. The action of GL(n,F) on the Grassmann variety Gr(m,n,F) induces a continuous representation of the maximal compact subgroup of GL(n,F) on the space of L^2-functions on Gr(m,n,F). The irreducible constituents of this…

This thesis studies modular forms from a classical and adelic viewpoint. We use this interplay to obtain results about the arithmetic of the Fourier coefficients of modular forms and their generalisations. In Chapter 2, we compute lower…

We give a lower bound for the sup-norm of an $L^2$-normalized newform in an irreducible, unitary, cuspidal representation $\pi$ of $GL_2$ over a number field. When the central character of $\pi$ is sufficiently ramified, this bound improves…

We show that every irreducible representation in the discrete automorphic spectrum of GL(n) admits a non vanishing mixed (Whittaker-symplectic) period integral. The analog local problem is a study of models first considered by Klyachko over…

We revisit the local metaplectic correspondence previously constructed and studied by Flicker and Kazhdan. After restoring and generalizing some of their results, we get several interesting applications to the representation theory of a…

In this article, we give explicit formulas of archimedean Whittaker functions on $GL(3)$ and $GL(2)$. Moreover, we apply those to the calculation of archimedean zeta integrals for $GL(3)\times GL(2)$, and show that the zeta integral for…

We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS). We…

We characterize the space of new forms for $\Gamma_0(m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$. To do that we find generators and relations for a $p$-adic Hecke algebra of…

The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…

We study the local zeta integrals attached to a pair of generic representations $(\pi,\tau)$ of $GL_n\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions…

Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_2(F)$ defined over the residue…

In this note, we give a formula for the Whittaker-Shintani functions for the p-adic symplectic groups, which is a generalization of the Zonal spherical functions and Whittaker functions. We then use the formula to give an alternative proof…

We convolve a theta function on an $n$-fold cover of $GL_3$ with an automorphic form on an $n'$-fold cover of $GL_2$ for suitable $n,n'$. To do so, we induce the theta function to the $n$-fold cover of $GL_4$ and use a Shalika integral. We…

We develop a (largely conjectural) theory of p-adic L-functions interpolating square roots of central L-values for automorphic forms on GSp(4) x GL(2) x GL(2), and a relation between these p-adic L-functions and families of Galois…