In the previous two chapters we exploited the simplicity of the power series for the function e z in order to establish the transcendence results of Hermite-Lindemann and then Lindemann-Weierstrass. In this chapter we describe the next stage in the evolution of classical transcendental number theory, which involves viewing e z as a function of a complex variable z and applying more sophisticated analytic techniques. We illustrate these new themes by establishing the transcendence of e π .
KeywordsPower Series Entire Function Rational Number Algebraic Number Integer Solution
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