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

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

Abstract

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 .

Keywords

Power Series Entire Function Elliptic Curve Function Field Formal Power Series 
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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