The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori-Matsumoto involution, this is equivalent also to the classification of the spherical unitary dual for type E. Together with [BM3], [Ba1] and [Ci1], this work completes the classification of the Whittaker Iwahori-spherical unitary dual, or equivalently, the spherical unita...

We give a construction of a wide class of modular symbols attached to reductive groups. As an application we construct a p-adic distribution interpolating the special values of the twisted Rankin-Selberg L-function attached to cuspidal automorphic representations π and σ of GLn and GLn−1 over a number field k. If π and σ are ordinary at p, our distribution is bounded and gives rise to a p-adic ...

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We ...

Motivated by the study of periods automorphic forms and relative trace formulae, we develop theory descent necessary to orbital integrals arising in fundamental lemma for a general class symmetric spaces over p-adic field F. More precisely, prove that connected space F enjoys notion topological Jordan decomposition, which may be independent interest, establish version Kazhdan played crucial rol...

We formulate a conjectural p-adic analogue of Borel’s theorem relating regulators for higher K-groups of number fields to special values of the corresponding ζ-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of the conj...

We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota– Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg’s exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, ...

For inner products de ned by a symmetric inde nite matrix p;q, canonical forms for real or complex p;q-Hermitian matrices, p;q-skew Hermitian matrices and p;q-unitary matrices are studied under equivalence transformations which keep the class invariant.

Let p be a prime number, and let f = ∑ n anq n denote a normalized cuspidal eigenform of weight k + 2 on Γ0(N) with p N . If f is a p-ordinary form, then by [1, 17] we can attach a p-adic L-function to f which interpolates special values of its L-series. On the other hand, if f is non-ordinary at p, we have two p-adic L-functions attached to f , one for each root of x − apx + p. These two roots...