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Continuous Functions on Discrete Valuation Rings

โœ Scribed by Koichi Tateyama

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
110 KB
Volume
75
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let R be a complete discrete valuation ring with finite residue field, let K be its quotient field. We construct polynomial functions .(n, a)(n=0, 1, ...) such that any continuous function f from R into K has the following expansion

where the sequence [a n ]/K is uniquely determined by f and satisfies that lim n ร„ a n =0. When K=Q p , if we replace .(n, a) by the binomial coefficient a(a&1) } } } (a&n+1)ร‚n! we have Mahler's expansion theorem.

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