Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673137 | Indagationes Mathematicae | 2013 | 15 Pages |
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 (bnâ{1,2,â¦,pâ1},anâN)(n=1,2,â¦) such that x=pa0b1+pa1b2+pa2b3+pa3b4+â±. A sample result that we prove is that if pn(n=1,2,â¦) denotes the sequences of rational primes, we have limNââ1Nân=1Napn(x)=ppâ1, 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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
J. HanÄl, A. JaÅ¡Å¡ová, P. Lertchoosakul, R. Nair,