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four exponentials conjecture
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(Conjecture)
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Four exponentials conjecture: Given four complex numbers $x_1,x_2,y_1,y_2$ , either $x_1/x_2$ or $y_1/y_2$ is rational, or one of the four numbers $\exp(x_i y_j)$ is transcendental.
This conjecture is stronger than the six exponentials theorem.
- 1
- Waldschmidt, Michel, Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 326. Springer-Verlag, Berlin, 2000. xxiv+633 pp. ISBN 3-540-66785-7.
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"four exponentials conjecture" is owned by Kevin OBryant.
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Cross-references: six exponentials theorem, stronger, conjecture, transcendental, numbers, rational, complex numbers
There is 1 reference to this entry.
This is version 4 of four exponentials conjecture, born on 2003-06-11, modified 2004-11-09.
Object id is 4349, canonical name is FourExponentialsConjecture.
Accessed 4446 times total.
Classification:
| AMS MSC: | 11J81 (Number theory :: Diophantine approximation, transcendental number theory :: Transcendence ) |
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Pending Errata and Addenda
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