Renato Augusto Tavares

Wirsching's Positive-Predecessor-Density Program: Proofs of Conjectures 1 and 3

Wirsching (2003) reduces uniform positive predecessor density for the $3n+1$ map to a chain of five conditions, organized into three conjectures. We prove two of them. Conjecture 1 concerns his path-counting generators: in the convolution carrying them to his Elka functions the partition weights grow subexponentially w...