Schanuel’s Conjecture

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 21 in Transcendental Numbers, 2014, pp 111-121 from Springer

Abstract: Abstract Schanuel’s Conjecture: Suppose α 1, …, α n are complex numbers which are linearly independent over ℚ $$\mathbb{Q}$$ . Then the transcendence degree of the field ℚ ( α 1 , … , α n , e α 1 , … , e α n ) $$\displaystyle{\mathbb{Q}(\alpha _{1},\ldots,\alpha _{n},e^{\alpha _{1}},\ldots,e^{\alpha _{n}})}$$ over ℚ $$\mathbb{Q}$$ is at least n.

Keywords: Schanuel; Conjecture; Linear Independence; Transcendence Degree; Algebraic Independence (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0832-5_21

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