About statistics of periods of continued fractions of quadratic irrationalities

Abstract

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 $q$, $p^2+q^2\le R^2$. Our results concern the average sum of period elements and Gauss--Kuzmin statistics as $R\to \infty$.

arXiv comment10 pages, 3 figures, 1 table

References in corpus (3)

• Statistics of incomplete quotients of continued fractions of quadratic irrationalities
• Symmetries of quadratic forms classes and of quadratic surds continued fractions. Part II: Classification of the periods' palindromes
• On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators

Cited by in corpus (1)

• Statistics of incomplete quotients of continued fractions of quadratic irrationalities