# Length of the period of a quadratic irrational

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Article

DOI: 10.1007/BF01763963

- Cite this article as:
- Podsypanin, E.V. J Math Sci (1982) 18: 919. doi:10.1007/BF01763963

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## Abstract

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).## Copyright information

© Plenum Publishing Corporation 1982