#### 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.*

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