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. Battistoni
Primo
;
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).
Periods length of continued fractions; quadratic surds;
Settore MATH-03/A - Analisi matematica
Settore MATH-02/A - Algebra
ott-2024
23-lug-2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1097511
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