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 root d. This allows to improve the existing results for the large deviations of T(d).
The first and second moments for the length of the period of the continued fraction expansion for d$\sqrt {d}$ [The first and second moments for the length of the period of the continued fraction expansion for √d ] / F. Battistoni, L. Grenié, G. Molteni. - In: MATHEMATIKA. - ISSN 0025-5793. - 70:4(2024 Oct), pp. e12273.1-e12273.12. [10.1112/mtk.12273]
The first and second moments for the length of the period of the continued fraction expansion for d$\sqrt {d}$ [The first and second moments for the length of the period of the continued fraction expansion for √d ]
F. BattistoniPrimo
;G. Molteni
Ultimo
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 root d. This allows to improve the existing results for the large deviations of T(d).File in questo prodotto:
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