Article ID Journal Published Year Pages File Type
4673137 Indagationes Mathematicae 2013 15 Pages PDF
Abstract
An analogue of the regular continued fraction expansion for the p-adic numbers for prime p was given by T. Schneider, such that for x in pZp, i.e. the open unit ball in the p-adic numbers, we have uniquely determined sequences (bn∈{1,2,…,p−1},an∈N)(n=1,2,…) such that x=pa0b1+pa1b2+pa2b3+pa3b4+⋱. A sample result that we prove is that if pn(n=1,2,…) denotes the sequences of rational primes, we have limN→∞1N∑n=1Napn(x)=pp−1, almost everywhere with respect to Haar measure. In the case where pn is replaced by n this result is due to J. Hirsh and L. C. Washington. The proofs rely on pointwise subsequence and moving average ergodic theorems.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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