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.

References

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.

Title	four exponentials conjecture
Canonical name	FourExponentialsConjecture
Date of creation	2013-03-22 13:40:51
Last modified on	2013-03-22 13:40:51
Owner	Kevin OBryant (1315)
Last modified by	Kevin OBryant (1315)
Numerical id	7
Author	Kevin OBryant (1315)
Entry type	Conjecture
Classification	msc 11J81
Synonym	4 exponentials
Related topic	sixexponentialstheorem
Related topic	exponentialfunction
Related topic	ExponentialFunction
Related topic	SixExponentialsTheorem