Home » Keyword index

algebraic independence


Number Theory » Analytic N.T.

Schanuel's Conjecture ★★★★

Author(s): Schanuel

Conjecture   Given any $ n $ complex numbers $ z_1,...,z_n $ which are linearly independent over the rational numbers $ \mathbb{Q} $, then the extension field $ \mathbb{Q}(z_1,...,z_n,\exp(z_1),...,\exp(z_n)) $ has transcendence degree of at least $ n $ over $ \mathbb{Q} $.

Keywords: algebraic independence

Posted by Charles
updated January 19th, 2010
3 comments
Number Theory

Algebraic independence of pi and e ★★★

Author(s):

Conjecture   $ \pi $ and $ e $ are algebraically independent

Keywords: algebraic independence

Posted by porton
updated April 29th, 2012
6 comments
Syndicate content