Transcendence conjecture for power towers of ultra-Liouville numbers
Let θ\thetaθ be the fixed point of x↦ξxx\mapsto \xi^xx↦ξx and define the iterated power towers by h1(ξ)=ξh_1(\xi)=\xih1(ξ)=ξ and hk+1(ξ)=ξhk(ξ)h_{k+1}(\xi)=\xi^{h_k(\xi)}hk+1(ξ)=ξhk(ξ) for k≥1k\geq 1k≥1. An ultra-Liouville numbe…