Schanuel's Conjecture
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Conjecture
Let $z_1, \cdots, z_n$ be complex numbers that are linearly independent over the rational numbers $\Q$.
Then:
- the extension field $\map \Q {z_1, \cdots, z_n, e^{z_1}, \cdots, e^{z_n} }$ has transcendence degree at least $n$ over $\Q$
where $e^z$ is the complex exponential of $z$.
Source of Name
This entry was named for Stephen Hoel Schanuel.