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) |
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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: |
05 Dec 2022 15:30 |
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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