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Schanuel’s Conjecture

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Abstract

Schanuel’s Conjecture: Suppose α 1, …, α n are complex numbers which are linearly independent over \(\mathbb{Q}\). Then the transcendence degree of the field

$$\displaystyle{\mathbb{Q}(\alpha _{1},\ldots,\alpha _{n},e^{\alpha _{1}},\ldots,e^{\alpha _{n}})}$$

over \(\mathbb{Q}\) is at least n.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada

    M. Ram Murty

  2. Chennai Mathematical Institute, Siruseri, Tamil Nadu, India

    Purusottam Rath

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  1. M. Ram Murty
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  2. Purusottam Rath
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Murty, M.R., Rath, P. (2014). Schanuel’s Conjecture. In: Transcendental Numbers. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0832-5_21

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