On the quantitative metric theory of continued fractions in positive characteristic

Poj Lertchoosakul , Nair Radhakrishnan

Abstract

Let F-q be the finite field of q elements. An analogue of the regular continued fraction expansion for an element alpha in the field of formal Laurent series over F-q is given uniquely by alpha = A(0)(alpha) + 1/A(1)(alpha) + 1/A(2)(alpha) + vertical bar (sic), where (A(n)(alpha))(n=0)(infinity) is a sequence of polynomials with coefficients in F-q such that deg(A(n)(alpha)) >= 1 for all n >= 1. In this paper, we provide quantitative versions of metrical results regarding averages of partial quotients. A sample result we prove is that, given any epsilon > 0, we have vertical bar A(1)(alpha) . . . A(N)(alpha)vertical bar(1/N) = q(q)/((q-1)) + o(N-1/2(log N)(3/2+epsilon)) for almost everywhere alpha with respect to Haar measure.
Author Poj Lertchoosakul (FMPI / IM)
Poj Lertchoosakul,,
- Institute of Mathematics
, Nair Radhakrishnan
Nair Radhakrishnan,,
-
Journal seriesProceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, (A 25 pkt)
Issue year2018
Vol61
No1
Pages283-293
Publication size in sheets0.5
Keywords in Englishcontinued fractions, metric theory of numbers
DOIDOI:10.1017/S0013091517000177
URL https://doi.org/10.1017/S0013091517000177
Languageen angielski
LicenseOther; published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)25
ScoreMinisterial score = 25.0, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, ArticleFromJournal
Publication indicators WoS Impact Factor: 2017 = 0.604 (2) - 2017=0.674 (5)
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