Hall 123

Gelfond-Schneider theorem

Neelam Kandhil

IMSc

In 1900, Hilbert posed a remarkable problem which states that if $\alpha$ and $\beta$ are algebraic numbers with $\alpha$ not equal to 0 and 1, $\beta$ irrational, then $\alpha^{\beta}$ is transcendental. We give a complete proof of this result which is now known as the Gelfond-Schneider theorem.