Conferències i seminaris setmanals curs 2016-17

Irrationality and transcendence of values of special functions

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Michel Waldschmidt

Resum

There is no general result on the irrationality or transcendence of values of analytic functions: one needs to restrict to special functions. A number of results are known concerning analytic functions satisfying differential equations: we survey such results, including values of the exponential function, of elliptic or more generally abelian functions, of modular functions. We also present recent results dealing with the values of the E and G functions introduced by Siegel in 1929.

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