# 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.

## 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.