Related papers: Analytic constructions of p-adic L-functions and E…

For any rational prime $p$, we define a certain $p$-stabilization of holomorphic Siegel Eisenstein series for the symplectic group ${\rm Sp}(2n)_{/\mathbb{Q}}$ of an arbitrary genus $n \ge 1$. In addition, we derive an explicit formula for…

In this paper, we calculate the ramified local integrals in the doubling method and present an integral representation of standard $L$-functions for classical groups. We explicitly construct local sections of Eisenstein series such that the…

Given a cusp form $f$ which is supersingular at a fixed prime $p$ away from the level, and a Coleman family $F$ through one of its $p$-stabilisations, we construct a $2$-variable meromorphic $p$-adic $L$-function for the symmetric square of…

Let p be an odd prime and g an integer greater or equal to 2. We prove that a finite slope Siegel cuspidal eigenform of genus g can be p-adically deformed over the g-dimensional weight space. The proof of this result relies on the…

We discuss several congruences satisfied by the coefficients of meromorphic modular forms, or equivalently, the $p$-adic behaviors of meromorphic modular forms under the $U_p$ operator, that are summarized from numerical experiments. In the…

For absolutely simple, finite-dimensional Lie algebras g of rank at least 2, defined over a local field of characteristic 0 and admitting a graduation: g=g(-2)+g(-1)+g(0)+g(1)+g(2) given by an element H such that 2H is simple, we construct…

We establish existence theorems for the image of the normalized character map of the $p$-adic Heisenberg algebra $S$ taking values in the algebra of Serre $p$-adic modular forms $M_p$. In particular, we describe the construction of an…

Following Schweiger's generalization of multidimensional continued fraction algorithms, we consider a very large family of $p$-adic multidimensional continued fraction algorithms, which include Schneider's algorithm, Ruban's algorithms, and…

In this paper, we study primeness and pseudo primeness of p-adic meromorphic functions. We also consider left (resp. right ) primeness of these functions. We give, in particular, sufficient conditions for a meromorphic function to satisfy…

The family of symmetric powers of an $L$-function associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and p-adic points of view. Here we examine one explicit such family from…

For \psi a nontrivial additive character on the finite field F_q, the map t \mapsto \sum_{x \in F_q} \psi(f(x)+tx) is the Fourier transform of the map t \mapsto \psi(f(t))$. As is well-known, this has a cohomological interpretation,…

Properties of analytic vectors in representations of SL(2,R) are used to give new bounds for the triple products recently considered by P. Sarnak. A conjecture of Sarnak about such products is proved. The results of this paper generalize…

We introduce an automorphism $\mathcal{S}$ of the space $C(\mathbb{Z}_p,\mathbb{C}_p)$ of continuous functions $\mathbb{Z}_p \rightarrow \mathbb{C}_p$ and show that it can be used to give an alternative construction of the $p$-adic…

Let $p$ be a prime and $\mathcal{K}$ be an imaginary quadratic field. In this paper we generalize a recent construction of a new type of $p$-adic $L$-function and $p$-adic Waldspurger formula by Andreatta-Iovita for $p$ non-split in…

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators \`a la Bernstein of the category of…

In this paper we introduce the new notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper $p$-harmonic functions. We then apply this to construct the…

In this paper we establish certain identities connecting $p$-adic hypergeometric functions with 4-th twisted Kloosterman sheaf sum. To prove these identities we express certain character sum over finite field in terms of special values of…

For a prime number p and a number field k, we first study certain etale cohomology groups with coefficients associated to a p-adic Artin representation of its Galois group, where we twist the coefficients using a modified Tate twist with a…

We refine and extend previous constructions of $p$-adic $L$-functions for Rankin-Selberg convolutions on $\GL(n)\times\GL(n-1)$ for regular algebraic representations over totally real fields. We also prove an intrinsic functional equation…

In the theory of automorphic descents developed by Ginzburg, Rallis and Soudry in [GRS11], the structure of Fourier coefficients of the residual representations of certain special Eisenstein series plays important roles. Started from…