• Corpus ID: 15767086

An Introduction to Irrationality and Transcendence Methods.

  title={An Introduction to Irrationality and Transcendence Methods.},
  author={Michel Waldschmidt},
In 1873 C. Hermite [6] proved that the number e is transcendental. In his paper he explains in a very clear way how he found his proof. He starts with an analogy between simultaneous diophantine approximation of real numbers on the one hand and analytic complex functions of one variable on the other. He first solves the analytic problem by constructing explicitly what is now called Padé approximants for the exponential function. In fact there are two types of such approximants, they are now… 
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Simultaneous approximation to values of the exponential function over the adeles
  • D. Roy
  • Mathematics
    Mathematische Annalen
  • 2020
We show that Hermite’s approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into
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A unified proof of the irrationality of the special values L(n, X), n > 1 an integer, of the beta L-function is put forward in this note. The first case of n = 2 seems to confirm that the Catalan
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1 J un 2 01 8 The Product eπ Is Irrational
This note shows that the product eπ of the natural base e and the circle number π is an irrational number.


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