The statistics of continued fractions

for polynomials over a finite field

Authors:
Christian Friesen and Doug Hensley

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2661-2673

MSC (1991):
Primary 11A55

DOI:
https://doi.org/10.1090/S0002-9939-96-03394-1

MathSciNet review:
1328349

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a finite field of order and polynomials of degrees respectively, there is the continued fraction representation . Let denote the number of such pairs for which and for . We give both an exact recurrence relation, and an asymptotic analysis, for . The polynomial associated with the recurrence relation turns out to be of P-V type. We also study the distribution of . Averaged over all and as above, this presents no difficulties. The average value of is , and there is full information about the distribution. When is fixed and only is allowed to vary, we show that this is still the average. Moreover, few pairs give a value of that differs from this average by more than

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Additional Information

**Christian Friesen**

Affiliation:
Department of Mathematics, Ohio State University, Marion Campus, Marion, Ohio 43302

Email:
friesen.4@osu.edu

**Doug Hensley**

Affiliation:
Department of Mathematics, Texas A& M University, College Station, Texas 77843

Email:
doug.hensley@math.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03394-1

Received by editor(s):
August 20, 1994

Received by editor(s) in revised form:
March 27, 1995

Communicated by:
William W. Adams

Article copyright:
© Copyright 1996
American Mathematical Society