Abstract
In this paper, we give a new proof of the theorem due to B. F. Skubenko providing an estimate of the ratio between lengths of periods for two real quadratic irrationalities of the same discriminant. Bibliography: 9 titles.
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REFERENCES
B. F. Skubenko, "The asymptotic distribution of integer points over a one-sheeted hyperboloid and ergodic theorems," Izv. Akad. Nauk. SSSR, Ser. Mat., 26, 721-752 (1962).
Yu. V. Linnik, Ergodic Properties of Algebraic Fields[in Russain], Leningrad (1967).
H. Iwaniec, "Fourier coefficients of modular forms of half-integral weight," Invent. Math., 87, 385-401 (1987).
W. Duke, "Hyperbolic distribution problems and half-integral weight Maass forms," Invent. Math., 92, 73-90 (1988).
E. P. Golubeva, "Geodesics on the upper half-plane and the distribution of quadratic irrationalities," Zap. Nauchn. Semin. POMI, 254, 28-55 (1998).
E. P. Golubeva, "On the length of the period of a quadratic irrationality," Mat. Sb., 123, 120-129 (1994).
B. A. Venkov, Elementary Number Theory[in Russian], Moscow-Leningrad (1937).
A. S. Pen and B. F. Skubenko, "An upper bound of the period of a quadratic irrationality," Mat. Zametki, 5, 413-417 (1969).
E. P. Golubeva, "Quadratic irrationalities with fixed length of the period of expansion into a continued fraction," Zap. Nauchn. Semin. LOMI, 196, 5-30 (1991).
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Golubeva, E.P. On Skubenko's Theorem on Cycles. Journal of Mathematical Sciences 110, 3032–3039 (2002). https://doi.org/10.1023/A:1015407908650
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DOI: https://doi.org/10.1023/A:1015407908650