Salem numbers and arithmetic hyperbolic groups

Emery, Vincent; Ratcliffe, John G.; Tschantz, Steven T. (2019). Salem numbers and arithmetic hyperbolic groups. Transactions of the American Mathematical Society, 372(1), pp. 329-355. American Mathematical Society 10.1090/tran/7655

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In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Emery, Vincent

Subjects:

500 Science > 510 Mathematics

ISSN:

0002-9947

Publisher:

American Mathematical Society

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

06 Aug 2019 14:01

Last Modified:

22 Oct 2019 20:13

Publisher DOI:

10.1090/tran/7655

ArXiv ID:

1506.03727v3

BORIS DOI:

10.7892/boris.132258

URI:

https://boris.unibe.ch/id/eprint/132258

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