6 problems

Uniform normality preservation under rational multiplication for dynamically generated basic sequences
arXiv@arxiv
Let $Q=(q_n)_{n\geq 1}$ be a dynamically generated basic sequence, and let $\mathcal{UN}(Q)$ denote the set of uniformly $Q$ -normal numbers. Uniform normality multiplication conjec…
Conjectureopencantor-series-expansions normality number-theory
0
Descriptive-complexity conjecture for nondeterministic dynamically generated basic sequences
arXiv@arxiv
Let $Q=(q_n)_{n\geq 1}$ be a nondeterministic dynamically generated basic sequence. Let $\mathcal{N}(Q)$ , $\mathcal{DN}(Q)$ , and $\mathcal{UN}(Q)$ denote the corresponding normalit…
Conjectureopencantor-series-expansions descriptive-set-theory normality
0
Normality equivalence conjecture for deterministic dynamically generated basic sequences
arXiv@arxiv
Let $Q=(q_n)_{n\geq 1}$ be a deterministic dynamically generated basic sequence. Write $\mathcal{N}(Q)$ for the set of $Q$ -normal numbers, $\mathcal{UN}(Q)$ for the uniformly $Q$ -n…
Conjectureopencantor-series-expansions dynamical-systems normality
0
Hotspot theorem conjecture for deterministic dynamically generated basic sequences
arXiv@arxiv
Let $Q=(q_n)_{n\geq 1}$ be a deterministic dynamically generated basic sequence. Let the strongest hotspot theorem refer to the assertion that the hotspot hypotheses imply membersh…
Conjectureopencantor-series-expansions dynamical-systems normality
1
Generalized Bergelson–Vandehey hotspot conjecture for dynamically generated basic sequences
arXiv@arxiv
Generalized hotspot conjecture. Under these assumptions, $y\in\mathcal{UN}(Q)$ . This would extend the strongest known hotspot criterion beyond the currently established hypotheses,…
Conjectureopencantor-series-expansions dynamical-systems normality
0
Existence conjecture for solutions in the region \mathscr{R}_t}
arXiv@arxiv
Existence conjecture. For every $t\in\mathbb{N}$ , there is a solution $(c_1,c_2,\ldots,c_t)\in\mathscr{R}_t$ to the unperturbed system
Conjectureopencantor-series-expansions normality number-theory
0

6 problems

Uniform normality preservation under rational multiplication for dynamically generated basic sequences

Descriptive-complexity conjecture for nondeterministic dynamically generated basic sequences

Normality equivalence conjecture for deterministic dynamically generated basic sequences

Hotspot theorem conjecture for deterministic dynamically generated basic sequences

Generalized Bergelson–Vandehey hotspot conjecture for dynamically generated basic sequences

Existence conjecture for solutions in the region \mathscr{R}_t}