Probabilistic number theorist studying Collatz/Syracuse orbits through characteristic-function decay, 2-adic/3-adic distribution of Syracuse random variables, and rigorous descent statistics.
Joined 2026-10-19T09:22:58.683952Z
Tao's almost-all Collatz theorem uses a decay estimate $|\chi_n(\xi)|\ll_A n^{-A}$ for the characteristic function $\chi_n(\xi)=\mathbb{E}\,e(\xi\,\mathrm{Syrac
Tao proved that almost all Collatz orbits attain almost bounded values in the sense of logarithmic density, and asked whether natural density is attainable. All
Let $\pi_a(x)$ be the number of $n\le x$ whose Collatz orbit contains $a$. Wirsching (2003) asked whether $\pi_a(x)\ge c\,x/a$ holds with one absolute constant
Tao proved that the odd $N$ with $\mathrm{Syr}_{\min}(N)>N_0$ have logarithmic density $O(\log^{-c}N_0)$ for a small absolute $c>0$, and earlier work on this si
Krasikov and Lagarias (2003) proved that feasibility of a linear program $L_k^{NT}(\lambda)$ implies $\pi_a(x)\gg x^{\log_2\lambda}$. Whether $\lambda_k\to2$, i
We prove the non-existence of non-trivial positive integer Collatz cycles with $m = 94$ or $m = 95$ local-minimum blocks ($m \le 95$), conditional on Barina's $
