The Schneider–Lang Theorem

M. Ram Murty and Purusottam Rath
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
Purusottam Rath: Chennai Mathematical Institute

Chapter Chapter 9 in Transcendental Numbers, 2014, pp 35-38 from Springer

Abstract: Abstract In 1934, A.O. Gelfond and T. Schneider Gelfond, A.O. Schneider, T. independently solved Hilbert’s Hilbert’s seventh problem 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 2 $$2^{\sqrt{2}}$$ is transcendental as well as the number e π , as is seen by taking β = i and α = −1.

Keywords: Seventh Problem; Algebraic Number; Strict Order; Schneider's Method; Abelian Functions (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0832-5_9

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