# 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 $\Q \left({z_1, \cdots, z_n, e^{z_1}, \cdots, e^{z_n}}\right)$ 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.