KFU. Card publication. About statistics of periods of continued fractions of quadratic irrationalities / E.Yu. Lerner // Functional Analysis and Other Mathematics, 2010, vol. 3, Issue 1, pp. 75-83. In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form x^2+px=q with integer p and q, p^2+q^2≤R^2. We prove a weak variant of Arnold conjectures about the Gauss-Kuzmin statistics with R→∞.

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ABOUT STATISTICS OF PERIODS OF CONTINUED FRACTIONS OF QUADRATIC IRRATIONALITIES / E.YU. LERNER // FUNCTIONAL ANALYSIS AND OTHER MATHEMATICS, 2010, VOL. 3, ISSUE 1, PP. 75-83. IN THIS PAPER WE ANSWER CERTAIN QUESTIONS POSED BY V.I. ARNOLD, NAMELY, WE STUDY PERIODS OF CONTINUED FRACTIONS FOR SOLUTIONS OF QUADRATIC EQUATIONS IN THE FORM X^2+PX=Q WITH INTEGER P AND Q, P^2+Q^2≤R^2. WE PROVE A WEAK VARIANT OF ARNOLD CONJECTURES ABOUT THE GAUSS-KUZMIN STATISTICS WITH R→∞.

Form of presentation

Articles in international journals and collections

Year of publication

2010

Authors, employees of KFU

Lerner Eduard Yulevich, author

Bibliographic description in the original language

About statistics of periods of continued fractions of quadratic irrationalities / E.Yu. Lerner // Functional Analysis and Other Mathematics, 2010, vol. 3, Issue 1, pp. 75-83. In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form x^2+px=q with integer p and q, p^2+q^2≤R^2. We prove a weak variant of Arnold conjectures about the Gauss-Kuzmin statistics with R→∞.

Annotation

Functional Analysis and Other Mathematics

Place of publication

Berlin / Heidelberg

The name of the journal

Functional Analysis and Other Mathematics

Publishing house

Springer

URL

http://link.springer.com/journal/11853/3/1/page/1#page-1

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=51319&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Lerner Eduard Yulevich	ru_RU
dc.date.accessioned	2010-01-01T00:00:00Z	ru_RU
dc.date.available	2010-01-01T00:00:00Z	ru_RU
dc.date.issued	2010	ru_RU
dc.identifier.citation	About statistics of periods of continued fractions of quadratic irrationalities / E.Yu. Lerner // Functional Analysis and Other Mathematics, 2010, vol. 3, Issue 1, pp. 75-83. In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form x^2+px=q with integer p and q, p^2+q^2≤R^2. We prove a weak variant of Arnold conjectures about the Gauss-Kuzmin statistics with R→∞.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=51319&p_lang=2	ru_RU
dc.description.abstract	Functional Analysis and Other Mathematics	ru_RU
dc.description.abstract	Functional Analysis and Other Mathematics	ru_RU
dc.language.iso	ru	ru_RU
dc.publisher	Springer	ru_RU
dc.title	About statistics of periods of continued fractions of quadratic irrationalities / E.Yu. Lerner // Functional Analysis and Other Mathematics, 2010, vol. 3, Issue 1, pp. 75-83. In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form x^2+px=q with integer p and q, p^2+q^2≤R^2. We prove a weak variant of Arnold conjectures about the Gauss-Kuzmin statistics with R→∞.	ru_RU
dc.type	Articles in international journals and collections	ru_RU