The first and second moment for the length of the period of the continued fraction expansion of sqrt(d)

Francesco Battistoni; Loic Grenié; Giuseppe Molteni

The first and second moment for the length of the period of the continued fraction expansion of sqrt(d)

Francesco Battistoni, Loic Grenié, Giuseppe Molteni^*

^*Autore corrispondente per questo lavoro

Risultato della ricerca: Contributo in rivista › Articolo in rivista

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).

Lingua originale	English
pagine (da-a)	N/A-N/A
Numero di pagine	12
Rivista	Mathematika
Stato di pubblicazione	Pubblicato - 2024

Keywords

continued fraction
moments

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title = "The first and second moment for the length of the period of the continued fraction expansion of sqrt(d)",

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).",

keywords = "continued fraction, moments, continued fraction, moments",

author = "Francesco Battistoni and Loic Greni{\'e} and Giuseppe Molteni",

year = "2024",

language = "English",

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journal = "Mathematika",

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T1 - The first and second moment for the length of the period of the continued fraction expansion of sqrt(d)

AU - Battistoni, Francesco

AU - Grenié, Loic

AU - Molteni, Giuseppe

PY - 2024

Y1 - 2024

N2 - 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).

AB - 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).

KW - continued fraction

KW - moments

KW - continued fraction

KW - moments

UR - http://hdl.handle.net/10807/286718

M3 - Article

SN - 0025-5793

SP - N/A-N/A

JO - Mathematika

JF - Mathematika

ER -

The first and second moment for the length of the period of the continued fraction expansion of sqrt(d)

Abstract

Keywords

Altri file e collegamenti

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