Related papers: On approximation of p-adic numbers by p-adic algeb…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian…
In this paper, we complete the long-standing challenge to establish a Khintchine-type theorem for arbitrary nondegenerate manifolds in $\mathbb{R}^n$. In particular, our main result finally removes the analyticity assumption from the…
We find upper and lower bounds on the number of rational points that are $\psi$-approximations of some $n$-dimensional $p$-adic integer. Lattice point counting techniques are used to find the upper bound result, and a Pigeon-hole principle…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
In this paper, we improve some transcendence results for $p$--adic continued fractions. In particular, we prove that palindromic and quasi--periodic $p$--adic continued fractions converge either to transcendental numbers or quadratic…
Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has been already developed sharply. We derive our theorem for numerically equivalent ample divisors by dint of the above theory step by…
We derive heuristically the approximate formula for the difference $\sqrt{p_{n+1}} - \sqrt{p_n}$, where $p_n$ is the n-th prime. We find perfect agreement between this formula and the available data from the list of maximal gaps between…
We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…
The aim of this note is to give a simpler proof of a result of Avsec, which states that $q$-Gaussian algebras have the complete metric approximation property.
In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.
In this paper, I generalize a previous one about hilbertian kernels and approximation theory
We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an…
A detailed presentation of Beilinson's approach to p-adic Hodge theory.
A short proof of the linear nested Artin approximation property of the algebraic power series rings is given here.
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
For any prime $p$ and real number and $\alpha$, the $p$-adic Littlewood Conjecture due to de Mathan and Teuli\'e asserts that \[\inf_{|m|\ge1}|m|_p\cdot |m|\cdot |\left\langle\alpha m\right\rangle|=0.\] Above, $|m|$ is the usual absolute…
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…
We propose a new frame work of $p$-adic neural network. Unlike the original $p$-adic neural network by S.\ Albeverio, A.\ Khrennikov, and B.\ Tirrozi using a family of characteristic functions indexed by hyperparameters of precision as…
Grothendieck's conjecture on p-curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all…