Related papers: $p$-adic $L$-functions for elliptic curves over gl…

We construct p-adic L-functions associated to cuspidal Hilbert modular eigenforms of parallel weight two in certain dihedral or anticyclotomic extensions via the Jacquet-Langlands correspondence, generalizing works of Bertolini-Darmon,…

We give a survey of a couple known constructions of $p$-adic $L$-functions including Iwasawa's construction from classical Stickelberger elements. We then construct "real" Stickelberger elements, i.e., explicit elements in the Galois group…

We present a general approach to establish algebraic functional equations for big Galois representations over multiple $\mathbb{Z}_p$-extensions. Our result is formulated in both Selmer group and Selmer complex settings, and encompasses a…

We prove a functional equation for the three-variable $p$-adic $L$-function attached to the Rankin-Selberg convolution of a Coleman family and a CM Hida family, which was studied by Loeffler and Zerbes. Consequentially, we deduce that an…

Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powers of f, thus verifying general conjectures of Dabrowski and…

This article extends our study of the geometry of the $p$-adic eigencurve at a point defined by a weight $1$ cuspform $f$ irregular at $p$ and having complex multiplication, and the implications in Iwasawa and in Hida theories. The novel…

Wan proved the rationality of partial toric $L$-functions using $\ell$-adic techniques. In this paper, we present a $p$-adic proof in the spirit of Dwork. We demonstrate that partial $L$-functions can be expressed as an alternating product…

For an elliptic curve A defined over a global function field K of characteristic p>0, the p-Selmer group of the Frobenius twist of A tends to have larger order than that of A. The aim of this note is to discuss this phenomenon.

Let $K$ be the function field of a curve $C$ over a $p$-adic field $k$. We prove that, for each $n, d \geq 1$ and for each hypersurface $Z$ in $\mathbb{P}^n_{K}$ of degree $d$ with $d^2 \leq n$, the second Milnor $K$-theory group of $K$ is…

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 compute the $L$-functions of a large class of algebraic curves, and verify the expected functional equation numerically. Our computations are based on our previous results on stable reduction to calculate the local $L$-factor and the…

The formula of the title relates $p$-adic heights of Heegner points and derivatives of $p$-adic $L$-functions. It was originally proved by Perrin-Riou for $p$-ordinary elliptic curves over the rationals, under the assumption that $p$ splits…

Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume…

We give a criterion in terms of p-adic Asai L-functions for a cuspidal automorphic representation of GL(2) over a real quadratic field to be a distinguished representation, providing a p-adic counterpart of a well-known theorem of Flicker…

Let $L/k$ be a finite abelian extension of an imaginary quadratic number field $k$. Let $\mathfrak{p}$ denote a prime ideal of $\mathcal{O}_k$ lying over the rational prime $p$. We assume that $\mathfrak{p}$ splits completely in $L/k$ and…

We formulate and for the most part prove a conjecture in the style of Mazur-Greenberg for the nonvanishing of central values of Rankin-Selberg $L$-functions attached to elliptic curves in abelian extensions of imaginary quadratic fields.…

For two distinguished prime $\ell$ and $p$, we prove a $\ell$-adic version of the Poisson formula for reductive $p$-adic groups. In order to do this we write an identity for the trace of regular representation and orbital integrals. Next we…

We study the Iwasawa $\lambda$-invariant of Dirichlet characters $\chi$ of arbitrary order for odd primes $p$. From special values of the $p$-adic $L$-function and its derivative we derive several novel and easily computable criteria to…

We generalize and simplify the constructions of Darmon-Rotger and Hsieh of an unbalanced triple product $p$-adic $L$-function $\mathscr{L}_p^f(\boldsymbol{f},\boldsymbol{g},\boldsymbol{h})$ attached to a triple…

Let $L/K$ be an extension of complete discrete valuation fields of positive characteristic, and assume that the residue field of $K$ is perfect. The residue field of $L$ is not assumed to be perfect. In this paper, we show that the…