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Length of the period of a quadratic irrational
 E. V. Podsypanin
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Let ξ be a real quadratic irrational of discriminant D=f^{2}D_{i}>0, where D_{i} is the fundamental discriminant of the field and h are the character and the number of classes of the field , respectively, and \(L\left( {1,\chi } \right) = \sum\limits_{n = 1}^\infty {\frac{{\chi \left( n \right)}}{n}} \) proves the following estimate for the length l of the period of the expansion of ξ into a continued fraction: where ω=1 if f=1 and ω=2 if f>1. A. S. Pen and B. F. Skubenko (Mat. Zametki, 5, No. 4, 413–482 (1969)) have proved this estimate in the case f=1, D_{1}≡0 (mod4).
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 82, pp. 95–99, 1979.
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 Title
 Length of the period of a quadratic irrational
 Journal

Journal of Soviet Mathematics
Volume 18, Issue 6 , pp 919923
 Cover Date
 19820401
 DOI
 10.1007/BF01763963
 Print ISSN
 00904104
 Online ISSN
 15738795
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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