# 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 FourExponentialsConjecture 2013-03-22 13:40:51 2013-03-22 13:40:51 Kevin OBryant (1315) Kevin OBryant (1315) 7 Kevin OBryant (1315) Conjecture msc 11J81 4 exponentials sixexponentialstheorem exponentialfunction ExponentialFunction SixExponentialsTheorem