Four Exponentials Conjecture

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of


is transcendental (Waldschmidt 1979, p. 3.5). The corresponding statement obtained by replacing y_1,y_2 with y_1,y_2,y_3 has been proven and is known as the six exponentials theorem.

See also

Hermite-Lindemann Theorem, Six Exponentials Theorem, Transcendental Number

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Finch, S. R. "Powers of 3/2 Modulo One." §2.30.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 194-199, 2003.Waldschmidt, M. Transcendence Methods. Queen's Papers in Pure and Applied Mathematics, No. 52. Kingston, Ontario, Canada: Queen's University, 1979.Waldschmidt, M. "On the Transcendence Method of Gelfond and Schneider in Several Variables." In New Advances in Transcendence Theory (Ed. A. Baker). Cambridge, England: Cambridge University Press, 1988.

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Four Exponentials Conjecture

Cite this as:

Weisstein, Eric W. "Four Exponentials Conjecture." From MathWorld--A Wolfram Web Resource.

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