Related papers: A control theorem for $p$-adic automorphic forms a…
The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain…
We introduce a $\mathbb{C}/\mathbb{Z}$-valued invariant of a foliated manifold with a stable framing and with a partially flat vector bundle. This invariant can be expressed in terms of integration in differential $K$-theory, or…
There are various reasons why a naive analog of the Maeda conjecture has to fail for Drinfeld cusp forms. Focussing on double cusp forms and using the link found by Teitelbaum between Drinfeld cusp forms and certain harmonic cochains, we…
In this paper we develop a theory of class invariants associated to $p$-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to…
Vologodsky's theory of $p$-adic integration plays a central role in computing several interesting invariants in arithmetic geometry. In contrast with the theory developed by Coleman, it has the advantage of being insensitive to the…
We propose a new approach to studying classical solutions of the Bellman equation and Master equation for mean field type control problems, using a novel form of the "lifting" idea introduced by P.-L. Lions. Rather than studying the usual…
We consider a hyperbolic Dirac-type operator with growing potential on a a spatially non-compact globally hyperbolic manifold. We show that the Atiyah-Patodi-Singer boundary value problem for such operator is Fredholm and obtain a formula…
We consider arbitrary algebraic families of lower order deformations of nondegenerate toric exponential sums over a finite field. We construct a relative polytope with the aid of which we define a ring of coefficients consisting of p-adic…
In numerical existence proofs for solutions of the semi-linear elliptic system, evaluating the norm of the inverse of a perturbed Laplace operator plays an important role. We reveal an eigenvalue problem to design a method for verifying the…
Let $\Pi$ be a regular algebraic cuspidal automorphic representation (RACAR) of $\mathrm{GL}_3(\mathbb{A}_{\mathbb{Q}})$. When $\Pi$ is $p$-nearly-ordinary for the maximal standard parabolic with Levi $\mathrm{GL}_1 \times \mathrm{GL}_2$,…
The purpose of this paper is to prove integrality for certain $p$-adic iterated Coleman integrals. As underlying geometry we will take the complement of a divisor $D\subset X$ with good reduction, where $X$ is the projective line or an…
We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q}) $ as $q\rightarrow p^{-}$, where $u_{q}$ is the…
In a separable Hilbert space $X$, we study the controlled evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where $A\geq-\sigma I$ ($\sigma\geq0$) is a self-adjoint linear operator, $B$ is a bounded linear…
This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative…
Parasupersymmetric quantum mechanics is exploited to introduce a topological invariant associated with a pair of parameter dependent Fredholm (respectively elliptic differential) operators satisfying two compatibility conditions. An…
The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine the validity of the so-called Ulam method, a numerical scheme…
In this article, we study $p$-adic torus periods for certain $p$-adic valued functions on Shimura curves coming from classical origin. We prove a $p$-adic Waldspurger formula for these periods, generalizing the recent work of Bertolini,…
The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…
This article presents an approach to the algebraic functional equation for Selmer complexes, which in turn have applications in the Iwasawa theoretic study of Rankin-Selberg products of the Hida and Coleman families. Our treatment…
Given a finite morphism $\varphi:Y\to X$ of quasi-smooth Berkovich curves over a complete, algebraically closed field $k$ of characteristic $0$, we prove a Riemann-Hurwitz formula relating their Euler-Poincar\'e characteristics (calculated…