Let d be any positive and non-square integer. We prove an upper bound for the first two moments of the length T(d) of the period of the continued fraction expansion for sqrt(d). This allows to improve the existing results for the large deviations of T(d).
Battistoni, F., Grenié, L., Molteni, G., The first and second moment for the length of the period of the continued fraction expansion of sqrt(d), <<MATHEMATIKA>>, 2024; (NA): N/A-N/A [https://hdl.handle.net/10807/286718]
The first and second moment for the length of the period of the continued fraction expansion of sqrt(d)
Battistoni, FrancescoCo-primo
;
2024
Abstract
Let d be any positive and non-square integer. We prove an upper bound for the first two moments of the length T(d) of the period of the continued fraction expansion for sqrt(d). This allows to improve the existing results for the large deviations of T(d).
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