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algebraic independence
Schanuel's Conjecture ★★★★
Author(s): Schanuel
Conjecture Given any
complex numbers
which are linearly independent over the rational numbers
, then the extension field
has transcendence degree of at least
over
.
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ z_1,...,z_n $](/files/tex/b7779accf6429c04a1809e479068a39e57552d59.png)
![$ \mathbb{Q} $](/files/tex/f360db0eb889cd59a651c1e7b4bc99fc86f6ee6c.png)
![$ \mathbb{Q}(z_1,...,z_n,\exp(z_1),...,\exp(z_n)) $](/files/tex/08d62d0ffdaba5b8acbe2a1e75839421fc8ac633.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ \mathbb{Q} $](/files/tex/f360db0eb889cd59a651c1e7b4bc99fc86f6ee6c.png)
Keywords: algebraic independence
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