The Statistics of Continued Fractions for Polynomials over a Finite Field

@inproceedings{Friesen1996TheSO,
  title={The Statistics of Continued Fractions for Polynomials over a Finite Field},
  author={Christian Friesen and Doug Hensley},
  year={1996}
}
Given a finite field F of order q and polynomials a, b ∈ F [X] of degrees m < n respectively, there is the continued fraction representation b/a = a1 + 1/(a2 + 1/(a3 + · · · + 1/ar)). Let CF (n, k, q) denote the number of such pairs for which deg b = n, deg a < n, and for 1 ≤ j ≤ r, deg aj ≤ k. We give both an exact recurrence relation, and an asymptotic analysis, for CF (n, k, q). The polynomial associated with the recurrence relation turns out to be of P-V type. We also study the distribution… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-6 of 6 references

Applications of Number Theory to Numerical Analysis

  • L. K. Hua, Y. Wang
  • Springer, Berlin
  • 1981
Highly Influential
5 Excerpts

The largest digit in the continued fraction expansion of a rational number

  • D. Hensley
  • Pacific Jour. Math. 151
  • 1991

The length of the continued fraction expansion for a class of rational functions in Fq(X)

  • A. Knopfmacher
  • Proc. Edinburgh Math. Soc. 34
  • 1991
1 Excerpt

Rational functions with partial quotients of small degree in their continued fraction expansion

  • H. Niederreiter
  • Monatshefte Math. 103
  • 1987

On the average length of a class of finite continued fractions

  • H. Heilbronn
  • Number Theory and Analysis, Plenum Press, New…
  • 1969
2 Excerpts

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