# 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