height of an algebraic number

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


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


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


  • 1 Shaw, R. Mathematics Society Notes, 1st edition. King’s School Chester, 2003.
  • 2 Stewart, I. Galois TheoryMathworldPlanetmath, 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