Related papers: p-adic L-functions of automorphic forms and except…

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…

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 x be a CM point on a modular or Shimura curve and p a prime of good reduction, split in the CM field K. We define an expansion of an holomorphic modular form f in the p-adic neighborhood of x and show that the expansion coefficients…

We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N \geq 5$ divisible by a prime number $p \neq 2$. Every $p$-adic representation of $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ associated to an eigenform is obtained…

We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series,…

Let $\mathbb{A}$ be the adele ring of a totally real algebraic number field $F$. We push forward an explicit computation of a relative trace formula for periods of automorphic forms along a split torus in $GL(2)$ from a square free level…

Let f be a modular form of weight k>=2 and level N, let K be a quadratic imaginary field, and assume that there is a prime p exactly dividing N. Under certain arithmetic conditions on the level and the field K, one can attach to this data a…

Let $\mathfrak{F}_m$ be the set of all cuspidal automorphic representations of $\mathrm{GL}_m(\mathbb{A}_{\mathbb{Q}})$, and let $F(s,\boldsymbol{\pi})$ be a polynomial in the derivatives of $L$-functions associated with representations…

We prove three main results: all Langlands-Shahidi automorphic $L$-functions over function fields are rational; after twists by highly ramified characters our automorphic $L$-functions become polynomials; and, if $\pi$ is a globally generic…

We study the restriction of the Bump-Friedberg integrals to affine lines $\{(s+\alpha,2s),s\in\C\}$. It has a simple theory, very close to that of the Asai $L$-function. It is an integral representation of the product…

Let G be a connected reductive quasisplit algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal…

Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun constructed a…

We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signature (r, 0) (for any positive integer r) for a quadratic…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

The question about modular forms have recently received a lot of attention; concerning the non-vanishing of automorphic L-functions Michel, Kowalski and Vanderkam proved (among others results) that there's positive proportion of…

Let G be a reductive algebraic group over a number field k. It is shown how Emerton's methods may be applied to the problem of p-adically interpolating the metaplectic forms on G, i.e. the automorphic forms on metaplectic covers of G, as…

We construct $p$-adic triple product $L$-functions that interpolate (square roots of) central critical $L$-values in the balanced region. Thus, our construction complements that of M. Harris and J. Tilouine. There are four central critical…

We study the action of the Galois group $G$ of a finite extension $K/k$ of number fields on the points on an elliptic curve $E$. For an odd prime $p$, we aim to determine the structure of the $p$-adic completion of the Mordell-Weil group…

In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good…

We study scattering processes on $p$-adic multiloop surfaces represented as multiloop infinite graphs with total valence in each vertex equal $p+1$. They all are spaces of the constant negative curvature since they are quotients of the…