Definition:Pisot-Vijayaraghavan Number
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Definition
Let $\alpha$ be a real algebraic integer greater than $1$.
Let $\alpha$ be such that the absolute values of its Galois conjugates are all less than $1$.
Then $\alpha$ is a Pisot-Vijayaraghavan number.
Also known as
A Pisot-Vijayaraghavan number is also known as:
- a Pisot number
- a PV number.
Also see
Source of Name
This entry was named for Charles Pisot and Tirukkannapuram Vijayaraghavan.
Historical Note
The Pisot-Vijayaraghavan numbers were discovered by Axel Thue in $1912$.
They were rediscovered by Godfrey Harold Hardy in $1919$ within the context of Diophantine approximation.
They became more widely known after the publication of Charles Pisot's dissertation in $1938$.
Tirukkannapuram Vijayaraghavan and Raphaël Salem continued their study in the $1940$s.
Sources
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,32471 795 \ldots$
- Terr, David and Weisstein, Eric W. "Pisot Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PisotNumber.html