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four exponentials conjecture


: Given four complex numbers x1,x2,y1,y2, either x1/x2 or y1/y2 is rational, or one of the four numbers exp(xiyj) is transcendental.

This conjecture is stronger than the six exponentials theorem.

References

  • 1 Waldschmidt, Michel, Diophantine approximation on linear algebraic groupsMathworldPlanetmath. Transcendence properties of the exponential functionDlmfDlmfMathworldPlanetmathPlanetmath 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 conjectureMathworldPlanetmath
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