КФУ. Карточка публикации. 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→∞.

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2010

Авторы, сотрудники КФУ

Лернер Эдуард Юльевич, автор

Библиографическое описание на языке оригинала

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→∞.

Аннотация

Functional Analysis and Other Mathematics

Место издания

Berlin / Heidelberg

Название журнала

Functional Analysis and Other Mathematics

Издательство

Springer

URL

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

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https://repository.kpfu.ru/?p_id=51319

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Лернер Эдуард Юльевич	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/?p_id=51319	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	Статьи в зарубежных журналах и сборниках	ru_RU