Abstract
The problem of classifying the indefinite binary quadratic forms with integer coefficients is solved by introducing a special partition of the de Sitter world, where the coefficients of the forms lie, into separate domains. Under the action of the special linear group acting on the integer plane lattice, each class of indefinite forms has a well-defined finite number of representatives inside each such domain.
In the second part, we will show how to obtain the symmetry type of a class and also the number of its points in all domains from a single representative of that class.
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Aicardi, F. Symmetries of quadratic form classes and of quadratic surd continued fractions. Part I: A Poincaré tiling of the de Sitter world. Bull Braz Math Soc, New Series 40, 301–340 (2009). https://doi.org/10.1007/s00574-009-0014-z
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DOI: https://doi.org/10.1007/s00574-009-0014-z