7 problems

Let $\mathsf{AMTV}_w$ be the $\mathbb{Q}$-vector space generated by all alternating multiple $T$-values of weight $w$, and write $d_w=\dim_{\mathbb{Q}}\mathsf{AMTV}_w$ for…

Parity-homogeneity conjecture. Every relation between alternating multiple $t$-values is homogeneous in $r$ modulo $2$; equivalently, terms involving an even number of negative sig…

Singular-parameter conjecture. Discounting the $\lambda_1=0$ term, the sequence satisfies: the sign of $\lambda_i$ is $(-1)^i$ for all $i>1$; the odd-indexed and even-indexed subse…

Basis conjecture. For any $0<\lambda<1$, the family

For ${\bf k}=(k_1,\ldots,k_r)\in\mathbb{N}^r$, let $\zeta_B^\star({\bf k})$ denote the multiple zeta-binomial-star value and let alternating multiple zeta values be multiple zeta v…

Consider alternating sums associated with the alphabet $\{A,B,C\}$, where $C=-d\log(1+x)$. Let $x$ record weight and $y$ record depth, and let primitive elements be filtered by bot…

Let $w$ be even and consider the depth-two MDV $\Re Z(A^{w-2}D^2)$. Let the relevant modular forms of weight $w$ and the corresponding alternating sums be those described by the so…