10 problems

Let $T_{r,\alpha}$ be the generalized Gauss continued-fraction map, and let $\lambda(r,\alpha)$ be the Lyapunov exponent of the orbit of $x_0\in[0,1]$ under $T_{r,\alpha}$. Let…

For powers-of-two moduli $2^k$, consider the modular Ackermann map $A_{2^k}(m,n)$ and its output distribution on $\mathbb Z_{2^k}$ as the recursion level $m$ varies. Hierarchy mixi…

Let $p$ be an odd prime, let $n=\lceil\log_2 p\rceil$, and let $\operatorname{Ext}_p:\mathbb{F}_p\times\mathbb{F}_p\to\{0,1\}$ be the Paley graph extractor defined from the quadrat…

Legendre 2-adic-complexity conjecture.

Omega correlation conjecture.

Omega linear-complexity conjecture.

The Sato–Tate independence conjecture. For every integer $s\geq1$, the sequence $\{X_k\}_{k\geq1}$ is uniformly distributed with respect to $\mu_{ST}^{[s]}$; equivalently,

New toy conjecture. The distributions $(S_1,\ldots,S_m)$ and $(T_1,\ldots,T_m)$ are computationally indistinguishable.

Toy conjecture. The distributions $(S_1,\ldots,S_m)$ and $(T_1,\ldots,T_m)$ are computationally indistinguishable.

For primes $p\equiv1\bmod4$, let $\chi$ be the Legendre symbol modulo $p$. Define $\operatorname{PaleyDiscrepancy}[\alpha,\beta]$ to mean that, for every sufficiently large $p$, ……