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Last year, in a talk of Michel Waldschmidt's, I remember hearing a statement along the lines of the title of this question, that is, "The Galois group of $\pi$ is $\mathbb{Z}$.". In what sense/framework is this true? What was meant exactly - and can this notion be made precise?

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Crossposted from math.SE: math.stackexchange.com/q/94994 –  Theo Buehler Dec 30 '11 at 2:52
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See this nice survey by Andre: arxiv.org/abs/0805.2569 –  user18237 Dec 30 '11 at 3:04
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@JSeaton: When you crosspost to/from math.SE, please inform readers (in both sites) of the fact; this helps prevent duplication of efforts. If you get a good answer in one site, please be sure to note it in the other. –  Arturo Magidin Dec 30 '11 at 4:29
    
@Arturo: Okay, noted. –  Joshua Seaton Dec 30 '11 at 16:31

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