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p-adic value

См. также в других словарях:

  • p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …   Wikipedia

  • P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

  • P-adic quantum mechanics — One may compute the energy levels for a potential well like this one.[note 1] P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p adic analysis to quantum… …   Wikipedia

  • Absolute value (algebra) — In mathematics, an absolute value is a function which measures the size of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping | thinsp; sdot; thinsp;| from D to the real… …   Wikipedia

  • p-adic exponential function — In mathematics, particularly p adic analysis, the p adic exponential function is a p adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse function named the p adic logarithm. Contents 1 …   Wikipedia

  • Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

  • p-adically closed field — In mathematics, a p adically closed field is a field that enjoys a closure property that is a close analogue for p adic fields to what real closure is to the real field. They were introduced by James Ax and Simon B. Kochen in 1965.[1] Contents 1… …   Wikipedia

  • 0.999... — In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0 …   Wikipedia

  • Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… …   Wikipedia

  • Bernoulli number — In mathematics, the Bernoulli numbers Bn are a sequence of rational numbers with deep connections to number theory. They are closely related to the values of the Riemann zeta function at negative integers. There are several conventions for… …   Wikipedia

  • Newton's method — In numerical analysis, Newton s method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real valued function. The… …   Wikipedia

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