Francesco Battistoni, Loïc Grenié, Giuseppe Molteni
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The first and second moments for the length of the period of the continued fraction expansion for
Let be any positive and non-square integer. We prove an upper bound for the first two moments of the length of the period of the continued fraction expansion for . This allows to improve the existing results for the large deviations of .
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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