On the quantitative metric theory of continued fractions in positive characteristic
Poj Lertchoosakul , Nair Radhakrishnan
AbstractLet 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.
|Journal series||Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, (A 25 pkt)|
|Publication size in sheets||0.5|
|Keywords in English||continued fractions, metric theory of numbers|
|License||Other; published final; ; with publication|
|Score||= 25.0, 24-07-2019, ArticleFromJournal|
|Publication indicators||: 2016 = 1.222; : 2017 = 0.604 (2) - 2017=0.674 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.