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Units of indefinite quaternion algebras

Published online by Cambridge University Press:  14 November 2011

J. H. H. Chalk
J. H. H. Chalk
Affiliation:
University of Toronto, Canada
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Synopsis

If ℍ is a rational indefinite quaternion algebra and T is an order of ℍ, let G+(T) denote the subgroup of units u ∊ T with norm n(u) = + 1. For a certain class of orders, Eichler has determined the measure μ(G+(T)) of G+(T), viewed as a Fuchsian group. This is extended to arbitrary orders by methods depending only upon classical number-theory and group theory. As an application, an estimate of the magnitude of a small non-trivial solution of the diophantine Pellian equation

is supplied and the restrictions on the integers D and P associated with previous work on this question are eliminated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 1-2 , 1980 , pp. 111 - 126
Copyright
Copyright © Royal Society of Edinburgh 1980

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