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ON SOME BEHAVIOR OF INTEGRAL POINTS ON A HYPERBOLA

  • Received : 2012.08.21
  • Published : 2013.07.31

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

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