Abstract
Let IFq((X −1 )) be the field of formal power series in X −1 over IFq, the field with q elements. Let f ∈ IF q((X −1 )) satisfy the irreducible polynomial Af 2 + Bf + C = 0, with Δ = B 2 − 4AC. let Per(f )b e the length of the period of the continued fraction expansion of f .I n this paper, we show that Per(f ) ≤ (q − 1)(2 √ q) deg Δ−2 . We also prove that if Q is a monic polynomial with even degree, then the length of the period of the continued fraction expansion of any square root of Q is less than (q − 1)(2 √ q) deg Q−1 .
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