29 problems

Let $n$ be a positive integer, let $\mathbb{F}\subset\mathbb{C}$ be a field, and let $p_{1},\ldots,p_{n},q_{1},\ldots,q_{n}$ be fixed positive integers satisfying conditions C(i)--…

Functional-equation conjecture. One has $m_p^R=m_{w-p}^R$ for all $p$, hence $m_{w/2}\equiv\dim V\pmod 2$, and: (1) $L(\iota R,s)$ extends to an entire function except for a single…

Let $\widehat G_{n-1}^n$ be the configuration space used to define the Grassmannian $n$-logarithm, and let $a_i,b_j$ be the maps on this space appearing in its functional equations…

Both-types invariance conjecture. The only such pairs are the quasi-arithmetic transforms

Let $x\in R^n$ and $t\in R^r$, let $\Omega\subseteq R^r$ be open, and consider distribution solutions of the functional equation (1.1) satisfying assumptions A-1 through A-5. Let…

Matkowski's conjecture. The function $f$ solves this equation if and only if there exist $a,b\in\mathbb{R}$ with $a\neq b$ such that

Let $G$ be a reductive group and let $V\in{\operatorname{Rep}}(G)$, with $V^\vee$ its dual representation. Let ${\mathcal{P}}_V^{\operatorname{norm}}$ denote the normalized period…

Halanay–Smith criterion. Let $M\in\mathcal G$. The following statements are equivalent:

Additive-map factorization conjecture. There exists a fixed element $q\in D$ such that

Let $O$ be a split-octonion algebra, and let $f:O\rightarrow O$ be an additive map. Write $O^\times$ for the set of invertible elements of $O$. Split-octonion extension conjecture.…

Let $d\geq 2$, let $d'$ denote the parameter used to define the overlap types, and let $w\in{\mathcal{D}}_{2d'}$. Let $\mathfrak{f}_{2,d}(\mathfrak{o})$ be the relevant free class-…

Let $m\geq5$ be a modulus of the form $m=3k+\{-1,0,1\}$ with $k\geq3$, and let $S_m(\rho\mid\sigma)$ be the multiple-sum functions indexed by integer vectors…

Let $k\geq 2$, let $a_1,\dots,a_k$ be elements for which the displayed multiple polylogarithms are defined, and let $\mathcal{L}_{2k}$ be the weight-$2k$ component of the Lie coalg…

Let $V$ be a finite-dimensional $\d835\dd34_p$-vector space with a continuous…

Let $H_n(s)$ be the function defined from the discrete-torus spectral zeta function by the asymptotic expansion … where … Here $\zeta(\Delta,s)$ is the spectral zeta function of th…

Let $M$ be a symmetric homogeneous mean that has an asymptotic power series expansion, and suppose that it fulfills the requirements of the open question from Farhi. Let $L_c$ deno…

Let $\Phi$ and $\Psi$ be linear data, and let $\gamma$ be a partial matching map as in the paper. Write $\Phi\vdash'^k_\gamma\Psi$ for entailment using the additional elementary el…

Let $\Phi$ and $\Psi$ be linear data, and let $\gamma\colon I^\Psi\to I^\Phi\times\{0,1\}$ be a partial function. Assume that whenever functions…

Functional equation conjecture. The function $\zeta(\mathcal X,s)$ should have a meromorphic continuation to all $s\in\mathbb C$ and satisfy

Solution conjecture. Every solution $f(z)$ of the Hirzebruch functional equation with $n>2$ and these initial conditions is a solution of the associated differential equation.

Let $X$ be a totally ordered Abelian group with respect to addition, and let $F:X^n\to X$ be an associative, idempotent, monotone function. The function $F$ is reducible if there e…

Goncharov's conjecture. There are rational functions $f_j(x,y,z)$ such that

The function-equation conjecture. The only such function is $f(x)=x$. The conjecture is presented as a sufficient condition for Furstenberg's conjecture on continuous ergodic…

Let $k\in\mathbb{N}$ and let $f:\mathbb{N}\to\mathbb{C}$ satisfy … for all $u,v\in\mathbb{N}$. Characterization conjecture. Exactly one of the following possibilities holds: (1)…

Constancy conjecture. Then $g$ is constant. The source presents this as a proposed extension of the assertion that non-constant outer solutions do not occur in the corresponding cl…