Counting and equidistribution in quaternionic Heisenberg groups
Abstract
We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over Q in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Cambridge University Press (CUP)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202206173455Use this for linking
Review status
Peer reviewed
ISSN
0305-0041
DOI
https://doi.org/10.1017/S0305004121000426
Language
English
Published in
Mathematical Proceedings of the Cambridge Philosophical Society
Citation
- Parkkonen, J., & Paulin, F. (2022). Counting and equidistribution in quaternionic Heisenberg groups. Mathematical Proceedings of the Cambridge Philosophical Society, 173(1), 67-104. https://doi.org/10.1017/S0305004121000426
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Copyright© 2022 Cambridge University Press (CUP)