Geometry of Integral Binary Hermitian Forms

Details Geometry of Integral Binary Hermitian Forms Geometry of Integral Binary Hermitian Forms

2011-04-08

arxiv.org/abs/1104.1474v2

Mathematics

Number Theory

Scientific paper

We generalize Conway's approach to integral binary quadratic forms on Q to study integral binary hermitian forms on quadratic imaginary extensions of Q. In Conway's case, an indefinite form that doesn't represent 0 determines a line ("river") in the spine T associated with SL(2,Z) in the hyperbolic plane. In our generalization, such a form determines a plane ("ocean") in Mendoza's spine associated with the corresponding Bianchi group SL(2,A) in hyperbolic 3-space.

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