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- Distribution_(number_theory) abstract "In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function.The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfyingWe shall call these ordinary distributions. They also occur in p-adic integration theory in Iwasawa theory.Let ... → Xn+1 → Xn → ... be a projective system of finite sets with surjections, indexed by the natural numbers, and let X be their projective limit. We give each Xn the discrete topology, so that X is compact. Let φ = (φn) be a family of functions on Xn taking values in an abelian group V and compatible with the projective system:for some weight function w. The family φ is then a distribution on the projective system X.A function f on X is "locally constant", or a "step function" if it factors through some Xn. We can define an integral of a step function against φ asThe definition extends to more general projective systems, such as those indexed by the positive integers ordered by divisibility. As an important special case consider the projective system Z/nZ indexed by positive integers ordered by divisibility. We identify this with the system (1/n)Z/Z with limit Q/Z.For x in R we let ⟨x⟩ denote the fractional part of x normalised to 0 ≤ ⟨x⟩ < 1, and let {x} denote the fractional part normalised to 0 < {x} ≤ 1.".
- Distribution_(number_theory) wikiPageExternalLink l30185r823104886.
- Distribution_(number_theory) wikiPageID "36785973".
- Distribution_(number_theory) wikiPageRevisionID "601857694".
- Distribution_(number_theory) subject Category:Algebra.
- Distribution_(number_theory) subject Category:Number_theory.
- Distribution_(number_theory) comment "In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function.The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfyingWe shall call these ordinary distributions. They also occur in p-adic integration theory in Iwasawa theory.Let ... → Xn+1 → Xn → ...".
- Distribution_(number_theory) label "Distribution (number theory)".
- Distribution_(number_theory) sameAs m.0t_cw26.
- Distribution_(number_theory) sameAs Q17097858.
- Distribution_(number_theory) sameAs Q17097858.
- Distribution_(number_theory) wasDerivedFrom Distribution_(number_theory)?oldid=601857694.
- Distribution_(number_theory) isPrimaryTopicOf Distribution_(number_theory).