Emery, Vincent; Ratcliffe, John G.; Tschantz, Steven T. (2019). Salem numbers and arithmetic hyperbolic groups. Transactions of the American Mathematical Society, 372(1), pp. 329355. 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 norbifold 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: 
00029947 
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 