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Jun 28, 2014 at 9:11 history edited GH from MO CC BY-SA 3.0
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Jun 28, 2014 at 9:04 comment added GH from MO @shadow10: I added more details. Of course the standard analytic form of Dirichlet's theorem on arithmetic progression suffices for the irrationality of $\alpha$, along the above lines. The result of Huxley-Iwaniec is deeper: I only displayed it because I mentioned that a sizable proportion of digits can be prescribed for infinitely many $p_i$'s.
Jun 28, 2014 at 9:02 history edited GH from MO CC BY-SA 3.0
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Jun 28, 2014 at 8:22 comment added shadow10 Could you elaborate a bit? I don't find your second sentence that obvious. Thanks.
Jun 28, 2014 at 7:51 history answered GH from MO CC BY-SA 3.0