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four exponentials conjecture

(Conjecture)

Four exponentials conjecture: Given four complex numbers , either or is rational, or one of the four numbers $\exp(x_i y_j)$ is transcendental.

Bibliography

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.

"four exponentials conjecture" is owned by Kevin OBryant.

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Other names:

4 exponentials

Keywords:

transcendental numbers

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Cross-references: six exponentials theorem, conjecture, transcendental, numbers, rational, complex numbers
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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 3570 times total.

Classification:

11J81 (Number theory :: Diophantine approximation, transcendental number theory :: Transcendence )

Pending Errata and Addenda

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