6 problems

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 $r\in\mathbf{Q}^{\times}$…

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

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…

For a Laurent polynomial $P\in\mathbb C[x_1^{\pm1},\ldots,x_n^{\pm1}]$, let $m(P)$ denote its logarithmic Mahler measure. Let $f_{3,15}$ and $f_{4,6}$ be the modular forms defined…

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…