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

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Paul

Posts: 398
Registered: 7/12/10
Re: Transcendence theory
Posted: Apr 5, 2013 4:54 AM
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On Friday, April 5, 2013 9:40:59 AM UTC+1, Paul wrote:
> 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.
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> Does anyone know of any real numbers r which have the following two properties?
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> 1) r is known to be algebraic.
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> 2) No one knows an explicit polynomial over Z for which r is a root.
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> Hmmm..
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> 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."
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> 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).
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> Thank You,
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> Paul Epstein


It occurs to me that, in any case, my example of the type of answer I didn't want doesn't solve my problem, so it's unnecessary to give it as an example of an undesirable type of answer.

The Goldbach example doesn't satisfy (2) because that r is a root of x(x - 1) = 0.

Paul



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