Related papers: A p-adic Eisenstein measure for vector-weight auto…

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…

We show that the systems of Hecke eigenvalues occurring in the spaces of Siegel modular forms (mod p) of fixed dimension g, fixed level N, and varying weight, are the same as the systems occurring in the spaces of Siegel cusp forms with the…

Let $P$ be a monic prime of $\mathbb F_q[\theta]$, we define the $P$-adic $L$-series associated with Anderson $t$-modules and prove a $P$-adic class formula \`a la Taelman linking a $P$-adic regulator, the class module and a local factor at…

The goal of this paper is to construct the p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant overconvergent Shintani lifting. The classical Shintani map is the Hecke-equivariant map from the…

We extend Tsuji's iterative construction of complete K\"ahler--Einstein metrics with negative scalar curvature to noncompact K\"ahler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a…

In this note, we consider discriminant forms that are given by the norm form of real quadratic fields and their induced Weil representations. We prove that there exists an isomorphism between the space of vector-valued modular forms for the…

In this paper, we define a natural metric on Aut(X*) and prove that the closure of the adding machine group, a subgroup of the automorphism group, is both isometric and isomorphic to the group of p-adic integers. So, we show that the group…

In a 2005 paper, Yang constructed families of Hilbert Eisenstein series, which when restricted to the diagonal are conjectured to span the underlying space of elliptic modular forms. One approach to these conjectures is to show the…

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…

We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$-theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we…

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor--Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the…

In earlier work, the first named author generalized the construction of Darmon-style $\mathcal{L}$-invariants to cuspidal automorphic representations of semisimple groups of higher rank, which are cohomological with respect to the trivial…

We provide a geometric Hodge-Tate map giving generic description of the overconvergent modular symbols of some p-adic (accessible) weight k, base-changed to C_p, in terms of overconvergent modular forms of weight k+2.

In this paper we establish certain identities connecting $p$-adic hypergeometric functions with 4-th twisted Kloosterman sheaf sum. To prove these identities we express certain character sum over finite field in terms of special values of…

Let $G$ be any connected reductive $p$-adic group. Let $K\subset G$ be any special parahoric subgroup and $V,V'$ be any two irreducible smooth $\overline {\mathbb F}_p[K]$-modules. The main goal of this article is to compute the image of…

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…

We address some questions posed by Goss related to the modularity of Drinfeld modules of rank 1 defined over the field of rational functions in one variable with coefficients in a finite field. For each positive characteristic valued…

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod $p$ Hilbert modular forms, by making use of modularity lifting theorems and computations in $p$-adic Hodge theory.

The slope of a p-adic overconvergent eigenform of weight k is the p-adic valuation of its U_p eigenvalue. We find the slope of all 2-adic finite slope overconvergent eigenforms of tame level 1 and weight 0. As a consequence we prove that…

In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…