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Schanuel's conjecture (Conjecture)

Let $ x_1, x_2, \ldots, x_n$ be complex numbers linearly independent over $ \mathbb{Q}$. Then the set

$\displaystyle \{x_1,x_2,\ldots,x_n,e^{x_1},e^{x_2},\ldots,e^{x_n}\}$    

has transcendence degree greater than or equal to $ n$.

Though seemingly innocuous, a proof of Schanuel's conjecture would prove hundreds of open conjectures in transcendental number theory.



"Schanuel's conjecture" is owned by mathcam. [ full author list (2) ]
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See Also: Lindemann-Weierstrass theorem

Other names:  Schanuel conjecture
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Cross-references: transcendental number, conjectures, hundreds, proof, linearly independent, complex numbers
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This is version 8 of Schanuel's conjecture, born on 2003-09-25, modified 2006-09-08.
Object id is 4739, canonical name is SchanuelsConjecutre.
Accessed 3234 times total.

Classification:
AMS MSC: 11F67 (Number theory :: Discontinuous groups and automorphic forms :: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols)
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