p-adic analytic
Definition.
Let be the field of complex -adic numbers (http://planetmath.org/ComplexPAdicNumbers). Let be a domain in . A function is -adic analytic if has a Taylor series (with coefficients in ) about each point that converges to the function in an open neighborhood of .
For example, the -adic exponential function (http://planetmath.org/PAdicExponentialAndPAdicLogarithm) is analytic on its domain of definition:
The study of -adic analytic functions is usually called -adic analysis and it is very similar to complex analysis in many respects, although there are important differences coming from the distinct topologies of and .
Title | p-adic analytic |
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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 | -adic analytic |
Related topic | Analytic |
Related topic | PAdicExponentialAndPAdicLogarithm |
Defines | -adic analysis |
Defines | p-adic analysis |