3 problems

Cowan's conjecture. For every pair of positive integers $m,n$,

For positive integers $d$ and $M$, let … where $\mu(p)$ is the Mahler measure, and define … Here $\mathcal{S}_{m,n}=\mathcal{S}_{m,n}(M)$ is the family of elliptic surfaces with fi…

Average-rank conjecture. The average rank is $1/2$.