On some properties of partial quotients of the continued fraction expansion of d with even period

Let d be a non-square positive integer such that the period of the continued fraction expansion of d is even. We give some relations between some properties of partial quotients of the continued fraction expansion of d , which emerge from numerical experiments.

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Bibliographic Details
Published inArchiv der Mathematik Vol. 114; no. 6; pp. 649 - 660
Main Authors Kawamoto, Fuminori, Kishi, Yasuhiro, Tomita, Koshi
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2020
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Quotients
Secondary 11R11
11R29
Primary 11A55
Class numbers
Real quadratic fields
Continued fractions
11R27
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Summary:Let d be a non-square positive integer such that the period of the continued fraction expansion of d is even. We give some relations between some properties of partial quotients of the continued fraction expansion of d , which emerge from numerical experiments.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-020-01434-7