Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496566 | Journal of Number Theory | 2005 | 31 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
David Fried,