11 problems

Boyd's conjecture. The set $L^\sharp$ is closed with respect to the Euclidean topology.

Deninger's conjecture.

Let $a(x),b(x)\in\mathbf{Z}[x]$, put $P(x,y)=a(x)(y^2+1)+b(x)y$, and let $g(x)$ be the polynomial associated with $P$ by the paper's discriminant construction, so that the correspo…

Permissible-polynomial conjecture. Every permissible polynomial is a Chinburg polynomial, with the displayed linear combination determined by its $(f_1,\ldots,f_s)$-permissibility.…

Chinburg's conjectures. For every fundamental discriminant $-f<0$, there exists a bivariate rational function $P\in\mathbf{Z}(x,y)$ and a rational number $r\in\mathbf{Q}^{\times}$…

Let $m(R)$ denote the Mahler measure of a non-zero rational function $R$, let $L'(\chi,-n)$ denote the derivative of the Dirichlet $L$-function associated with a character $\chi$,…

Let $m(P)$ denote the Mahler measure of a non-zero polynomial $P$, let $L'(\,\cdot\,,-n)$ denote the derivative of a Dirichlet $L$-function, and let…

Modular $L$-value count conjecture. The value $n_2(-143360-101376\sqrt{2})$ should involve two modular $L$-values, while…

Let $m_2(t)$ be the two-variable Mahler measure studied in the paper, and let $f_{289}$ and $f_{17}$ be the normalized newforms whose initial Fourier expansions are given in the so…

Let … denote the third logarithmic Mahler measure of the polynomial $1+x+y$, and let $\operatorname{Ls}_4$ and $\operatorname{Cl}_s$ denote the log-sine and Clausen functions, resp…

Fermat-family divisibility conjecture. For this family, all of