Survey article: Seventy years of Salem numbers
arXiv:1408.0195 · doi:10.1112/blms/bdv027
Abstract
I survey results about, and recent applications of, Salem numbers.
25 pages, 1 figure. v3 is expanded and corrected version of v2, thanks to additional reader feedback. Also slightly amended title
References in corpus (9)
- On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number
- A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices
- There are Salem numbers of every trace
- Growth series of some hyperbolic graphs and Salem numbers
- Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers
- Integer symmetric matrices having all their eigenvalues in the interval [-2,2]
- Salem numbers and Pisot numbers via interlacing
- Multifractal analysis of Bernoulli convolutions associated with Salem numbers
- Salem numbers from a class of star-like trees
Cited by in corpus (10)
- On the number of roots of self-inversive polynomials on the complex unit circle
- Polynomials with symmetric zeros
- SU(2)-cyclic surgeries and the pillowcase
- How to count the number of zeros that a polynomial has on the unit circle?
- On distribution modulo 1 of the sum of powers of a Salem number
- Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups
- A proof of the Conjecture of Lehmer
- Isometries of lattices and automorphisms of K3 surfaces
- Cyclotomic Points and Algebraic Properties of Polygon Diagonals
- Multiplicities in the length spectrum and growth rate of Salem numbers