Reduction theory over quadratic imaginary fields |
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Authors: | David Fried |
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Institution: | Department of Mathematics, Boston University, 111 Cummington St., Boston MA 02215, USA |
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Abstract: | Hurwitz developed a reduction theory for real binary quadratic forms of positive discriminant based on least-remainder continued fractions. For each quadratic imaginary field k, we develop a similar theory for complex binary quadratic forms of nonzero discriminant. This uses a Markov partition for the geodesic flow over the quotient of hyperbolic 3-space by the Bianchi group Bk. When k has a Euclidean algorithm, our theory is based on least-remainder continued fractions. |
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Keywords: | Quadratic forms Continued fractions Bianchi groups Symbolic dynamics Markov partitions |
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