\(1 + \frac{1}{{{T^2} - T}} + \frac{1}{{({T^4} - T){{({T^2} - T)}^2}}} + \frac{1}{{({T^8} - T){{({T^4} - T)}^2}{{({T^2} - T)}^4}}} + \cdots \)

Transcending Numbers and Discovering a More Formal e: Function fields and the transcendence of eC(1)
  • Edward B. Burger
  • Robert Tubbs


We conclude our tour of classical transcendental number theory by transcending the world of numbers themselves and ascending to the realm of formal power series. Specifically, we consider transcendence issues within the setting of function fields in a single variable over a finite field. While this theory has important implications in many different areas of mathematics, our goal here is to discover an object in this context that is analogous to the all-important exponential function e z .


Power Series Entire Function Elliptic Curve Function Field Formal Power Series 
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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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