Definition:Salem Number
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Definition
A Salem number is a real algebraic integer $\alpha$ such that:
- $\alpha > 1$
- its conjugate roots all have absolute value no greater than $1$, at least one of which has absolute value exactly $1$.
Also known as
The Salem numbers are also known as the Salem constants.
Also see
- Definition:Salem Constant, believed to be the smallest Salem number.
Source of Name
This entry was named for Raphaël Salem.
Sources
- 1933: D.H. Lehmer: Factorisation of certain cyclotomic functions (Ann. Math. Ser. 2 Vol. 34: pp. 461 – 479) www.jstor.org/stable/1968172
- 1945: R. Salem: Power Series with Integral Coefficients (Duke Math. J. Vol. 12: pp. 153 – 172)
- 1977: David W. Boyd: Small Salem Numbers (Duke Math. J. Vol. 44: pp. 315 – 328)
- 1978: David W. Boyd: Pisot and Salem Numbers in Intervals of the Real Line (Math. Comp. Vol. 32: pp. 1244 – 1260) www.jstor.org/stable/2006349
- 1978: C.L. Stewart: Algebraic Integers whose Conjugates Lie Near the Unit Circle (Bull. Soc. Math. France Vol. 106: pp. 169 – 176)
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,17628 081 \ldots$
- Weisstein, Eric W. "Salem Constants." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SalemConstants.html