# Quadratic irrationals with fixed period length in the continued fraction expansion

Article

DOI: 10.1007/BF02111323

- Cite this article as:
- Golubeva, E.P. J Math Sci (1994) 70: 2059. doi:10.1007/BF02111323

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## Abstract

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

$$\sqrt D = \left[ {b_0 ,\overline {l_1 ,...,l_L ,...,l_1 ,2b_0 } } \right]$$

_{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.## Copyright information

© Plenum Publishing Corporation 1994