Related papers: $p$-adic $L$-functions on metaplectic groups

In this work we study $p$-adic continuous functions in several variables taking values on $\mathbb{Z}_p$. We describe the orthonormal van der Put base of these functions and study various Lipschitz conditions in several variables,…

In this article, we proove that it is equivalent for a generic irreducible representation of GL(n,K), with K a p-adic field, to be distinguished, and for its Rankin-Selberg Asai L-function to have an exceptional pole at zero. This extends a…

We come back to the construction of p-adic L-functions attached to cusp forms of even weight k in the spirit of G. Stevens, R. Pollack [7] and M. Greenberg [3] with a new unified presentation including the non-ordinary case. This…

Continuing the study of the Iwasawa theory of symmetric powers of CM modular forms at supersingular primes begun by the first author and Antonio Lei, we prove a Main Conjecture equating the "admissible" $p$-adic $L$-functions to…

We are studing Galois actions on fundamental groups. Using towers of coverings we construct measures on the products of finite copies of Z_p. Using these measures we can calculate coefficients of Galois representations. In the simplest case…

We continue with our study of the non-critical exceptional zeros of Katz' $p$-adic $L$-functions attached to a CM field $K$, following two threads. In the first thread, we redefine our (group-ring-valued) $\mathcal{L}$-invariant associated…

The use of overconvergent cohomology in constructing $p$-adic $L$-functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been established in a number of settings. The method is compatible…

We study the special values of the triple product $p$-adic $L$-function constructed by Darmon and Rotger at all classical points outside the region of interpolation. We propose conjectural formulas for these values that can be seen as…

In this paper we prove the Miyawaki conjecture related to the spinor $L$--function of a Siegel cusp form of weight 12 and degree 3 as a special example of results related to Miyawaki lifts of odd degree.

Let $E/\mathbb{Q}$ be an elliptic curve and let $p$ be an odd prime of good reduction for $E$. Let $K$ be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which $p$ splits. The goal of this paper is two-fold:…

Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of…

We use higher Coleman theory to construct a new $p$-adic $L$-function for $\text{GSp}_4 \times \text{GL}_2$. While previous works by the first author, Pilloni, Skinner and Zerbes had considered the $p$-adic variation of classes in the $H^2$…

Let f be a modular form of weight k and Nebentypus $\psi$. By generalizing a construction of Dabrowski and Delbourgo, we construct a p-adic L-function interpolating the special values of the L-function $L(s,\mathrm{Sym}^2(f)\otimes \xi)$,…

We establish a rationality result for the twisted Asai L-values attached to a Bianchi cusp form and construct distributions interpolating these L-values. Using the method of abstract Kummer congruences, we then outline the main steps needed…

Let $p$ be an odd prime and $L/K$ a $p$-adic Lie extension whose Galois group is of the form $\mathbb{Z}_p^{d-1}\rtimes \mathbb{Z}_p$. Under certain assumptions on the ramification of $p$ and the structure of an Iwasawa module associated to…

We formulate and prove an analogue of the non-commutative Iwasawa Main Conjecture for $\ell$-adic representations of the Galois group of a function field of characteristic $p$. We also prove a functional equation for the resulting…

Let R be a complete discrete valuation ring, S=R[[u]] and n a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection of sub-S-modules of S^d. As S is not principal, it…

Following a strategy suggested by Michel--Venkatesh, we study the cubic moment of automorphic $L$-functions on $\operatorname{PGL}_2$ using regularized diagonal periods of products of Eisenstein series. Our main innovation is to produce…

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 establish a duality result proving the `functional equation' of the characteristic ideal of the Selmer group associated to a nearly ordinary Hilbert modular form over the cyclotomic $\mathbb{Z}_{p}$ extension of a totally real number…