[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.4.1243

ON SOME BEHAVIOR OF INTEGRAL POINTS ON A HYPERBOLA

Kim, Yeonok (Department of Mathematics SoongSil University)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 1243-1259 More about this Journal

Abstract

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$ . We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.

Keywords

Kac-Moody algebra; hyperbolic type; integral point; Binet formula; Catalan's identity;

Citations & Related Records

Reference

1	R. A. Dunlap, The golden ratio and Fibonachi numbers, World Science, 1997.
2	A. J. Feingold, A hyperbolic GCM Lie algebra and the Fibonachi numbers, Proc. Amer. Math. Soc. 80 (1980), 379-385. DOI ScienceOn
3	A. F. Horadam, A Generalized the Fibonachi Sequence, Proc. Amer. Math. Monthly. 68 (1961), 455-459. DOI ScienceOn
4	V. G. Kac, Infinite-Dimensional Lie Algebras, Cambridge University Press, 1990.
5	S. J. Kang and D. J. Melville, Rank 2 Symmetric Hyperbolic Kac-Moody Algebras, Nagoya Math. J. 140 (1995), 41-75. DOI
6	J. Moragado, Some remark on an identy of Catalan concerning the Fibonachi numbers, Portugaliae Math. Soc. 39 (1980), 341-348.
7	K. S. Rao, Some Propertities of Fibonachi numbers, Amer. Math. Monthly. 60 (1953), 680-684. DOI ScienceOn