9 problems

Let $\operatorname{\mathbf{IKM}}(a,b;n)$ denote the corresponding on-shell Bessel moment, and let $\zeta_{7,1}(2)$ denote the multiple zeta value appearing in the Broadhurst–Mellit…

Broadhurst's conjecture.

Sum rule conjecture. For each pair of integers $(n,k)$ with $n\geq 2k\geq 2$, the following combination of Bessel moments vanishes:

Let $k$ be an odd integer, and let $G_{2k+2}^{\mathrm{BR}}$ be a Gröbner basis generating the Broadhurst–Roberts ideal … Let $\mathbf N_k$ be the matrix of on-shell Bessel moments.…

Broadhurst–Roberts quadratic relation conjecture. The matrices satisfy

Fix an integer $k$ and let $\Ppairing_k^\BR$ and $\Bpairing_k^\BR$ be the period and Betti intersection matrices associated with the Bessel moments. The Betti intersection pairing…

Let $\Motive_k$ be the motive considered in the paper, and let its field of periods and motivic Galois group be understood in the usual sense. Grothendieck's period conjecture. The…

Let $I_0(t)=\frac{1}{\pi}\int_0^\pi e^{t\cos\theta}\operatorname{d}\theta$ and $K_0(t)=\int_0^\infty e^{-t\cosh u}\operatorname{d}u$ for $t>0$. Bailey–Borwein–Broadhurst–Glasser co…

B$^3$G sum rule. For every such pair $(n,k)$, the sum vanishes identically: