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Dec 20, 2012 at 5:44 comment added intuilog This is great input and I will be looking into this in detail! (By the way I am currently trying to narrow down my interests and this is exactly the kind of feed back that I was looking for). However, a quick look into this tells me that it is expected (conjectured by who?) that $e$ and $\frac{1}{\pi}$ are not in fact periods. I have edited my original question to include more background, and while I feel like periods would be examples of the numbers I am considering, I may actually be thinking of a larger collection.
Dec 19, 2012 at 8:25 history edited ACL CC BY-SA 3.0
Corrected definition, added link to Yoshinaga's paper.
Dec 19, 2012 at 8:08 history answered ACL CC BY-SA 3.0