Integral binary Hamiltonian forms and their waterworlds
Abstract
We give a graphical theory of integral indefinite binary Hamiltonian forms f analogous to the one by Conway for binary quadratic forms and the one of Bestvina-Savin for binary Hermitian forms. Given a maximal order O in a definite quaternion algebra over Q, we define the waterworld of f, analogous to Conway's river and Bestvina-Savin's ocean, and use it to give a combinatorial description of the values of f on O×O. We use an appropriate normalisation of Busemann distances to the cusps (with an algebraic description given in an independent appendix), and the SL2(O)-equivariant Ford-Voronoi cellulation of the real hyperbolic 5-space.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society (AMS)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202302021606Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1088-4173
DOI
https://doi.org/10.1090/ecgd/362
Language
English
Published in
Conformal Geometry and Dynamics
Citation
- Parkkonen, J., & Paulin, F. (2021). Integral binary Hamiltonian forms and their waterworlds. Conformal Geometry and Dynamics, 25(7), 126-169. https://doi.org/10.1090/ecgd/362
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Additional information about funding
This work was supported by the French-Finnish CNRS grant PICS No. 6950. The second author greatly acknowledges the financial support of Warwick University for a one month stay, decisive for the writing of this paper.
Copyright© Authors 2021