Related papers: $p$-adic $L$-functions for $\mathrm U(2,1)\times\m…

We construct $p$-adic $L$-functions interpolating the critical values of the degree eight $L$-functions of ${\rm GSp}(4)\times {\rm GL}(2)$ for cuspidal automorphic representations generated by $p$-ordinary Siegel modular forms of genus two…

By using q-Volkenborn integral on Z_{p}, we (simsek, simsekCanada) constructed new generating functions of the (h,q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to the generating functions, we constructed…

Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of $p$-adic $L$-functions (of Bella\"iche and Stevens) over the eigencurve. As the first ingredient, we…

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…

We define a two-variable $p$-adic Asai $L$-function for a finite-slope family of Hilbert modular forms over a real quadratic field (with one component of the weight, and the cyclotomic twist variable, varying independently); and a…

We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian type in the anticyclotomic direction for both root numbers. When the root number is $+1$, the construction relies on global Bessel periods on…

The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class of Rankin-Selberg tensor products. Although the conjecture is not proved in full…

In [Pollack-Stevens 2011], efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of $p$-adic $L$-functions and have further been applied to compute rational…

We study the variation of mu-invariants in Hida families with residually reducible Galois representations. We prove a lower bound for these invariants which is often expressible in terms of the p-adic zeta function. This lower bound forces…

We construct an Euler system of $p$-adic zeta elements over the eigencurve which interpolates Kato's zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable…

We p-adically interpolate the relative de Rham cohomology of the universal elliptic curve over strict neighbourhoods of the ordinary locus of modular curves, together with the Hodge filtration and Gauss-Manin connection. Sections of these…

We construct the anticyclotomic $p$-adic $L$-function that interpolates a square root of central values of twisted spinor $L$-functions of a quadratic base change of a Siegel cusp form of genus $2$ with respect to a paramodular group of…

We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent cohomology of Siegel threefolds in positive degrees. We…

In this article, we present a new linear independence criterion for values of the $p$-adic polygamma functions defined by J.~Diamond. As an application, we obtain the linear independence of some families of values of the $p$-adic Hurwitz…

Let M be an imaginary quadratic field, f a Hecke eigenform on GL2(Q) and \pi the unitary base-change to M of the automorphic representation associated to f. Take a unitary arithmetic Hecke character \chi of M inducing the inverse of the…

We give a new construction of a $p$-adic $L$-function $\mathcal{L}(f,\Xi)$, for $f$ a holomorphic newform and $\Xi$ an anticyclotomic family of Hecke characters of $\mathbb{Q}(\sqrt{-d})$. The construction uses Ichino's triple product…

This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg $p$-adic $L$-functions in universal deformation families. Starting from residual representations $\bar\rho_1,\bar\rho_2$ of tame…

In this paper, we prove an "explicit reciprocity law" relating Howard's system of big Heegner points to a two-variable $p$-adic $L$-function (constructed here) interpolating the $p$-adic Rankin $L$-series of Bertolini-Darmon-Prasanna in…

Let F be a totally real number field. Using a recent geometric approach developed by Andreatta and Iovita we construct several variables p-adic families of finite slope quaternionic automorphic forms over F. It is achieved by interpolating…

We give a new and representation theoretic construction of $p$-adic interpolation series for central values of self-dual Rankin-Selberg $L$-functions for $\operatorname{GL}_2$ in dihedral towers of CM fields, using expressions of these…