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Journal of Mathematical Sciences
, Volume 70, Issue 6, pp 20592076
First online:
Quadratic irrationals with fixed period length in the continued fraction expansion
 E. P. Golubeva
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We present an algorithm that makes it possible to write out all quadratic irrationals of the form\(\sqrt D \), that have a given even period length in the continued fraction expansion. It turns out that in the expansion λ={l_{1}, ..., l_{L+1}} is almost arbitrary, and b_{0} (and, consequently D) runs through a very narrow sequence depending on λ. We obtain a summation formula for the class numbers of indefinite binary forms with discriminant D with D≤X for which the set λ is fixed.
$$\sqrt D = \left[ {b_0 ,\overline {l_1 ,...,l_L ,...,l_1 ,2b_0 } } \right]$$
 Title
 Quadratic irrationals with fixed period length in the continued fraction expansion
 Journal

Journal of Mathematical Sciences
Volume 70, Issue 6 , pp 20592076
 Cover Date
 199408
 DOI
 10.1007/BF02111323
 Print ISSN
 10723374
 Online ISSN
 15738795
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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