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Topic: Transcendence theory
Replies: 2   Last Post: Apr 5, 2013 5:33 AM

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Posts: 603
Registered: 7/12/10
Transcendence theory
Posted: Apr 5, 2013 4:40 AM
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I'll admit up front that this post makes me definitely guilty of a near-repetition of something I posted earlier. This time, I think I have a clearer phrasing of what I want -- hence the repetition.

Does anyone know of any real numbers r which have the following two properties?

1) r is known to be algebraic.
2) No one knows an explicit polynomial over Z for which r is a root.

I thought that was a really clear statement of what I'm trying to find. But it isn't because someone could say "r where r = the truth value (either 0 or 1) of the statement of the Goldbach conjecture."

But that's not the type of thing I mean. I'm thinking of numbers which are given by an explicit series like eta(3).

Thank You,

Paul Epstein

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