Related papers: P-adic integration on ray class groups and non-ord…

Let $p$ be an odd prime and $F_{\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group $G$. Suppose that $G$ is a compact pro-$p$ $p$-adic Lie group with no torsion and that it contains a closed normal subgroup $H$ such…

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 show that the finite part of the adjoint $L$ function (including contributions from all nonarchimedean places, including ramified places) is holomorphic in $\Re(s) \ge 1/2$ for a cuspidal automorphic representation of $GL_3$ over a…

We investigate generalizations along the lines of the Mordell--Lang conjecture of the author's $p$-adic formal Manin--Mumford results for $n$-dimensional $p$-divisible formal groups $\mathcal{F}$. In particular, given a finitely generated…

We prove automorphy lifting results for certain essentially conjugate self-dual $p$-adic Galois representations $\rho$ over CM imaginary fields $F$, which satisfy in particular that $p$ splits in $F$, and that the restriction of $\rho$ on…

Let $\Pi$ be a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A_Q})$ and let $p$ be an odd prime at which $\Pi$ is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded $p$-adic…

Let $p$ be a prime, $k$ a finite extension of $\mathbf{F}_p$ of cardinal $q$, $l$ a finite extension of $k$ of group $\Sigma=\mathrm{Gal}(l|k)$, and $T$ a subgroup of $l^\times$. Using the method of "little groups", we classify irreducible…

This paper is third in a series of three, following "Summation Formulas, from Poisson and Voronoi to the Present" (math.NT/0304187) and "Distributions and Analytic Continuation of Dirichlet Series" (math.FA/0403030). The first is primarily…

Let $\Pi$ be a regular algebraic cuspidal automorphic representation (RACAR) of $\mathrm{GL}_3(\mathbb{A}_{\mathbb{Q}})$. When $\Pi$ is $p$-nearly-ordinary for the maximal standard parabolic with Levi $\mathrm{GL}_1 \times \mathrm{GL}_2$,…

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…

We study zeta functions enumerating finite-dimensional irreducible complex linear representations of compact p-adic analytic and of arithmetic groups. Using methods from p-adic integration, we show that the zeta functions associated to…

Let $p\geq 3$ be a prime number and $K$ be a quadratic imaginary field in which $p$ splits as $\mathfrak{p}\overline{\mathfrak{p}}$. Let $\mathcal{F}$ be a cuspidal Bianchi eigenform over $K$ of weight $(k,k)$, where $k\geq 0$ is an…

Given primes $\ell\ne p$, we record here a $p$-adic valued Fourier theory on a local field over $\mathbf{Q}_\ell$, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex…

From a spectral identity we obtain asymptotics with error term for the second integral moments of families of automorphic L-functions for GL(2) over an arbitrary number field according to twists by idele characters with arbitrary…

Let $K$ be an imaginary quadratic field, with associated quadratic character $\alpha$. We construct an analytic $p$-adic $L$-function interpolating the twisted adjoint $L$-values $L(1, \mathrm{ad}(f) \otimes \alpha)$ as $f$ varies in a Hida…

Let $K/F$ be a quadratic extension of $p$-adic fields, and $n$ a positive integer. A smooth irreducible representation of the group $GL(n,K)$ is said to be distinguished, if it admits on its space a nonzero $GL(n,F)$-invariant linear form.…

We extend the work of Ash and Stevens [Ash-Stevens 97] on p-adic analytic families of p-ordinary arithmetic cohomology classes for GL(N,Q) by introducing and investigating the concept of p-adic rigidity of arithmetic Hecke eigenclasses. An…

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…

Let $p$ be a prime number and $K$ a finite extension of $\mathbb{Q}_p$. We state conjectures on the smooth representations of $\mathrm{GL}_n(K)$ that occur in spaces of mod $p$ automorphic forms (for compact unitary groups). In particular,…

In this note we extend some of the results of a previous paper \url{arXiv:math/0511593} to algebraically closed fields of finite characteristic. In particular, we show that there is an explicit expression in $n$ and $d$ which is divisible…