Nathan Humphrey's writings
2026-06-02 analytic number theory doi · 10.5281/zenodo.20514168

Closed-Form Plancherel Mass of the Syracuse Stationary Measure: The Constant 7/45

by Nathan Humphrey
abstract

Let πk denote the stationary distribution of Tao's Syracuse Markov chain on the multiplicative group (Z/3kZ)*, and let Sk = Σ |µ̂k(ξ)|² be the associated high-frequency Plancherel mass. We identify the leading constant in the level-deviation norm |dk|² · 3k−1 → c, with c = 7/45.

read full paper on zenodo doi.org/10.5281/zenodo.20514168
cite
APA Humphrey, N. (2026). Closed-Form Plancherel Mass of the Syracuse Stationary Measure: The Constant 7/45. Zenodo. https://doi.org/10.5281/zenodo.20514168
BibTeX 
@misc{humphrey-2026-plancherel,
  author    = {Nathan Humphrey},
  title     = {Closed-Form Plancherel Mass of the Syracuse Stationary Measure: The Constant 7/45},
  year      = {2026},
  month     = {jun},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.20514168},
  url       = {https://doi.org/10.5281/zenodo.20514168}
}