Abstract
In 1934, A.O. Gelfond and T. Schneider independently solved Hilbert’s seventh problem. This problem predicted that if α and β are algebraic numbers with α ≠ 0, 1 and β irrational, then α β is transcendental. In particular, the number \(2^{\sqrt{2}}\) is transcendental as well as the number e π, as is seen by taking β = i and α = −1.
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Murty, M.R., Rath, P. (2014). The Schneider–Lang Theorem. In: Transcendental Numbers. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0832-5_9
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DOI: https://doi.org/10.1007/978-1-4939-0832-5_9
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