相关论文: Notes on p-adic numbers
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
In this paper, we study Catalan numbers which can be represented by the p-adic integral on Zp and we investigate some properties and formulae related to Catalan numbers and special numbers.
The purpose of this paper is to give the explicit formulae of p-adic l-functions and sums of powers which are related to Euler numbers.
Some question about representations of $p$-adic groups are discussed.
In this short paper I consider relation between measurements, numbers and p-adic mathematical physics. p-Adic numbers are not result of measurements, but nevertheless they play significant role in description of some systems and phenomena.…
In this paper, we offer a brief introduction to the $p$-adic numbers and operations in the metric space defined under the $p$-adic norm. Specifically, we provide a clear description of the derivation of the $p$-adic number via the…
Some p-adic series with factorials are considered.
Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.
This paper first introduces the concept of p-adic number and field. Then it develops the p-adic integration and applied it to solve p-adic Schrodinger equations.
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…
A brief review of some selected topics in p-adic mathematical physics is presented.
These informal notes deal with p-adic versions of Heisenberg groups and related matters.
These are the notes from my courses on the arithmetic of quadratic forms.
Let $p$ be a prime. We discuss $p$-adic properties of various arithmetical functions related to the coefficients of modular form and generating functions. Modular forms are considered as a tool of solving arithmetical problems. Examples of…
A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.
The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.