11 problems

Let $\gamma_k^B$ denote the Bernoulli matching-model limiting constant for alphabet size $k$. Boutet de Monvel's conjecture. … The source presents this as a conjecture about the as…

For alphabet size $k$, let $\gamma_k^B$ be the Bernoulli matching-model limiting constant and let $\gamma_k$ be the corresponding random-string-model limiting constant. Equality co…

Boutet de Monvel's conjecture. The Bernoulli matching-model growth constant satisfies the displayed formula. Boutet de Monvel also gave a more general conjecture for off-diagonal l…

Dominance threshold conjecture. As $d\to\infty$, for every fixed $p>0.1$, the probability that the random homogeneous ideal is dominant tends to $0$.

Arguin, Dubach, and Hartung's conjecture concerns the maximum of a random model of the Riemann zeta function over intervals whose lengths vary between the IID and log-correlated re…

Let $T>1$, let $\tau$ be chosen uniformly from $[T,2T]$, and let $0<\alpha<1$ with $\theta\sim(\log\log T)^{-\alpha}$. Consider an interval of size … The smoothing-scale conjecture…

Domination conjecture. The first random model should be dominated by the second random model in the same sense: the second random model should have higher moments of every order an…

Let $\operatorname{RM}$ be the random model, with a realisation determined by the shifts $a$ and factors $\rho_k(n+a)$, and let $\pi_{\operatorname{RM}}(x)$ be its counting functio…

Let $\operatorname{RM}_c$ be the constrained random model, and let $\pi_{\operatorname{RM}_c}(x)$ denote the associated counting function for a realisation. Let…

Let ${\operatorname{RM}}_c$ denote the constrained ${\operatorname{RM}}$ described in the source, and let $\pi_{\operatorname{RM}_c}(x)$ be its prime-counting function. Let…

Typical short-interval maximum conjecture. Let $\epsilon>0$. For $T_1$ sufficiently large depending on $\epsilon$, for all $T_1\leq T\leq 2T_1$, outside a set of “bad” values of…