Schanuel's Conjecture

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.