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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

Abstract

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.

Keywords

Measure Zero Algebraic Number Infinite Sequence Minimal Polynomial Irreducible Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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