p-adic analytic


Let Cp be the field of complex p-adic numbers (http://planetmath.org/ComplexPAdicNumbers). Let U be a domain in Cp. A functionMathworldPlanetmath f:UCp is p-adic analyticPlanetmathPlanetmath if f has a Taylor seriesMathworldPlanetmath (with coefficients in Cp) about each point zU that converges to the function f in an open neighborhood of z.

For example, the p-adic exponential functionDlmfDlmfMathworldPlanetmath (http://planetmath.org/PAdicExponentialAndPAdicLogarithm) is analytic on its domain of definition:


The study of p-adic analytic functions is usually called p-adic analysisMathworldPlanetmath and it is very similar to complex analysis in many respects, although there are important differencesPlanetmathPlanetmath coming from the distinct topologies of and p.

Title p-adic analytic
Canonical name PadicAnalytic
Date of creation 2013-03-22 15:13:53
Last modified on 2013-03-22 15:13:53
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 4
Author alozano (2414)
Entry type Definition
Classification msc 11S99
Classification msc 12J12
Classification msc 11S80
Synonym p-adic analytic
Related topic Analytic
Related topic PAdicExponentialAndPAdicLogarithm
Defines p-adic analysis
Defines p-adic analysis