334 problems

Let $calpha>2$ be real, and let $c_{n,k}$ and the associated quantities be those defined in the paper. All-α conjecture. The statement of Theorem cref{t:super4} holds true for ever…

Let $\rho\in\mathbb{N}$, and assume (A1) obtained from the preceding lemma. Let $(a_k)_{k\geqslant 0}$ be the sequence defined by the two Nesterov equations referred to in the sour…

Let $f^\beta(x)$ be the unique solution of equation (2) with $f^\beta(0)=1$. Asymptotic growth conjecture. As $x\to+\infty$, the function $f^\beta$ should be asymptotic to … for a…

Let $u_r$ be the symmetric homogeneous polynomial coordinates in $N$ variables constructed in the main theorem. For a partition $\sigma\vdash r$ and a differential operator of orde…

Determinant-asymptotics conjecture. The leading asymptotics is given by

Fix $\beta>0$. Let $g:\mathbb{R}\to\mathbb{R}$ be $2\pi$-periodic and belong to $C^{1,q}$ for some $0<q\leq 1$, let $t\in\mathbb{R}$, and let $I$ denote the integral whose normaliz…

Linear upper bound conjecture. As $n\to\infty$, $ML(n)=O(n)$.

Let $l$ be an odd positive integer, and let $a_l^l$ denote the coefficient in the expansion of the solution referred to as Expansion. Classicality criterion. The solution with odd…

Asymptotic ratio conjecture. The limit exists:

Asymptotic expansion conjecture. For a large class of boundary conditions $\mathbf{u}^{*}$, respectively source terms $\boldsymbol{f}$, there exists a solution of the body problem,…

For $\alpha>0$, let $A(\alpha)$ be the asymptotic constant conjectured for … and let $B(\alpha)$ be the corresponding constant when $|z_k|=1$. Equality of asymptotic constants conj…

Exact unit-circle asymptotic conjecture. One can choose $B(\alpha)=\underline B(\alpha)=\overline B(\alpha)$ in Theorem $avs$. This conjecture would close the gap between the known…

Exact asymptotic formula conjecture. One can choose $A(\alpha)=\underline A(\alpha)=\overline A(\alpha)$ in Theorem $u77$. This would determine the true asymptotic constant for eve…

Asymptotic constant conjecture. There exists a constant $1\leq c\leq\sqrt e$ such that

Asymptotic expansion conjecture. As $N\to\infty$ and $k\to\infty$ with $u$ fixed,

Let an SR sphere mean a sphere for a sub-Riemannian structure, and call the case non-integrable when the associated geodesic dynamics is not integrable. Il'Yashenko's category is t…

Let $n$ be the dimension parameter, let $\rho=(n-1)/2$, and let $F(a,b;c;z)$ denote the hypergeometric function. For the function $F_k(z)=F(k,-\rho;k+n/2;z)$, with complex variable…

Generalized spiral limit conjecture. The rescaled functions $p_k\left(z_0+\frac{z}{\sqrt{k}}\right)$ have a subsequence converging to a normalization of $P_\lambda$ for some…

Let $X$ be a Seifert manifold with base $S^2$, and let $(l,\underline{n}')\in\mathcal I_2^b$. Suppose that there do not exist elements $g_1,\ldots,g_n\in\operatorname{SU}(2)$ satis…

Let $p/q$ be a rational surgery coefficient, let $d$ be the inverse of $p$ modulo $q$, let $(a,b)\in\{0,1\}^2$, $n\in\mathbb{Z}/|q|\mathbb{Z}$, and $(\mu,\nu)\in\{\pm1\}^2$. Define…

Let $\mathcal{Q}_N$ denote the configuration space of $N$ points in three-dimensional space, and let $F_N$ be the angular sum defined in the paper. The asymptotic spherical-distrib…

Let $p_{n+1}(z)=\sum_{i=1}^{k}Q_i(z)p_{n-i}(z)$ be a finite recurrence with fixed polynomial coefficients, and suppose $\deg p_n(z)=n$ for $n\in\mathbb N$. Let $\Xi_Q$ be the equim…

Let $m$ be the complex dimension, let $m\leq q\leq 2m$, and let $Y_{2m-q}$, $\Delta(\lambda)$, $\Delta(\xi)$ and the integration variables be as in the source's preceding definitio…

Asymptotic conjecture for $(2,k,k)$-numbers. For each $k$,

Heuristic exponent conjecture for $(2,1,2)$-numbers.