13 problems

König's conjecture. For each Banach space $F$ with non-trivial type, there exists an $s$ with $2<s<\infty$ such that

Analyticity criterion for C-Summation. If this series is analytic at $-\frac{k_2}{k_1}$, then $I_n$ is suitable for C-Summation.

Non-closure conjecture. The set of sequences preserving summability is not closed under addition.

Ring-morphism conjecture. The map $f\mapsto \mathcal{S}_{q}^{d}(f)$ defines a morphism of rings.

Ring-morphism conjecture. The map $f\mapsto \mathcal{S}_{q}^{d}(f)$ defines a morphism of rings; in particular, it preserves products whenever both sides are defined:

Let $f(n)$ be an arithmetic function, let $p_n$ denote the $n$th prime, and let $\operatorname{idx}(p_n)=n$. Suppose that the Cesàro mean … exists. Prime-indexed Abelian limit conj…

Let $\mathbb{R}_+=(0,\infty)$, let $\mathcal{K}^{\infty}$ denote the class of functions that are completely convex, and let $\mathcal{D}^{\infty}_{\mathbb{N}}$ denote the class of…

Let $\omega$ denote an infinite hyperreal, and consider evaluating infinite series by discrete integral formulas. An additive offset of $\omega$ is an infinite index whose parity i…

Let $\Phi:[0,\infty)\to[0,\infty)$ be a continuous increasing function with $\Phi(0)=0$, and suppose that … For $f\in L\log L(\mathbb{T}^2)$, write $S_{ij}(x_1,x_2,f)$ for the rect…

Summability conjecture. There is a normalizing transformation that is summable with respect to $y^2-x^3$.

Consider a completely integrable Pfaffian system with normal crossings whose two monomial exponents are $(p,q)$ and $(p',q')$, and let $A_{0,0}$ and $B_{0,0}$ denote the matrices o…

Bender–Weniger conjecture. The factorially divergent perturbation expansion of this non-Hermitian $\mathcal{PT}$-symmetric anharmonic oscillator is a Stieltjes series.

Let $(C,\delta)$ denote the Cesàro means of order $\delta$ of the hexagonal Fourier series. Convergence conjecture. The $(C,\delta)$ means of the hexagonal Fourier series should co…