The Statistics of Continued Fractions for Polynomials over a Finite Field

  title={The Statistics of Continued Fractions for Polynomials over a Finite Field},
  author={Christian Friesen and Doug Hensley},
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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