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Date: 27-8-2020
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Date: 14-11-2019
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Date: 16-7-2020
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Let and
be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of
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is transcendental (Waldschmidt 1979, p. 3.5). The corresponding statement obtained by replacing with
has been proven and is known as the six exponentials theorem.
REFERENCES:
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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