Gelfond–Schneider theorem

The Gelfond–Schneider theorem is a fundamental result in transcendental number theory, established by Aleksandr Gelfond and Richard Schneider in the 1930s.

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For algebraic

a \neq = 0, 1

and algebraic irrational

b

, every value

exp (bλ)

with

e^{λ} = a

is transcendental. Consequently any quotient of chosen nonzero logarithms of algebraic numbers is either rational or transcendental.