Salem number Guide, Meaning , Facts, Information and Description
In mathematics, a real algebraic integer is a Salem number if all its conjugate roots have absolute value no greater than , and at least one has absolute value exactly . Salem numbers are of interest in diophantine approximation and harmonic analysis. They are named for Raphaël Salem (1898-1963).It can be shown that all the conjugate roots of a Salem number have absolute value exactly one, except one which has absolute value . As a consequence it must be a unit in the ring of algebraic integers, being of norm 1. Because it has a root of absolute value 1, the minimal polynomial for a Salem Number must be reciprocal.
The smallest known Salem number is the largest real root of the polynomial
- .
See also: Pisot-Vijayaraghavan number, Mahler measure.
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