 So in this case the conjecture would imply that at least one of "e", "e""π", and "e""π" ² is transcendental (which in this case is already known since "e" is transcendental).The conjecture was considered as early as the early 1940s by Atle Selberg who never formally stated the conjecture.A special case of the conjecture is mentioned in a 1944 paper of Leonidas Alaoglu and Paul Erdős who suggest that it had been considered by Carl Ludwig Siegel.