height of an algebraic number

Suppose we have an algebraic number such that the polynomial of smallest degree it is a root of (with the co-efficients relatively prime) is given by:

\sum_{i=0}^{n}a_{i}x^{i}.

Then the height $h$ of the algebraic number is given by:

h=n+\sum_{i=0}^{n}|a_{i}|.

This is a quantity which is used in the proof of the existence of transcendental numbers.

References

1 Shaw, R. Mathematics Society Notes, 1st edition. King’s School Chester, 2003.
2 Stewart, I. Galois Theory, 3rd edition. Chapman and Hall, 2003.
3 Baker, A. Transcendental Number Theory, 1st edition. Cambridge University Press, 1975.

Title	height of an algebraic number
Canonical name	HeightOfAnAlgebraicNumber
Date of creation	2013-03-22 13:24:34
Last modified on	2013-03-22 13:24:34
Owner	kidburla2003 (1480)
Last modified by	kidburla2003 (1480)
Numerical id	17
Author	kidburla2003 (1480)
Entry type	Definition
Classification	msc 03E10
Synonym	height
Related topic	AlgebraicNumbersAreCountable