2.718281828459… + 0.11000100000…

Class Distinctions Among Complex Numbers: Mahler’s classification and the transcendence of \( e + \sum\nolimits_{n = 1}^\infty {{{10}^{ - n!}}} \)
  • Edward B. Burger
  • Robert Tubbs


Polynomials with integer coefficients play a central role in the theory of transcendence. In fact, they made their first appearance at the very opening of our story—A number is transcendental precisely when it is not a zero of any nonzero polynomial in ℤ[z]. In this chapter, given an arbitrary complex number ξ, we forgo the fascination of determining whether there exists a nonzero polynomial that vanishes at ξ.


Measure Zero Algebraic Number Infinite Sequence Minimal Polynomial Irreducible Polynomial 
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Copyright information

© E.B. Burger and R. Tubbs 2004

Authors and Affiliations

  • Edward B. Burger
    • 1
  • Robert Tubbs
    • 2
  1. 1.Department of MathematicsWilliams CollegeWilliamstownUSA
  2. 2.Department of MathematicsUniversity of Colorado at BoulderBoulderUSA

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