The Collatz Conjecture & Non-Archimedean Spectral Theory: Part I -- Arithmetic Dynamical Systems and Non-Archimedean Value Distribution Theory

Maxwell Charles Siegel

Let $q$ be an odd prime, and let $T_q:\mathbb{Z}\to \mathbb{Z}$ be the Shortened $qx+1$ map, defined by $T_q\left(n\right)=n/2$ if $n$ is even and $T_{q}\left(n\right)=\…