4 problems

Weighted Erdős–Burgess equality conjecture.

Weighted Erdős–Burgess lower-bound conjecture.

For an integer $n>1$, let $I_r(\mathbb{Z}/n\mathbb{Z})$ denote the Erdős–Burgess constant of the multiplicative semigroup $\mathbb{Z}/n\mathbb{Z}$, let $\mathsf{D}(G)$ be the Daven…

Let ${\rm C}_{k;n}$ be a cyclic commutative semigroup with parameters $k$ and $n$, and let ${\hat{\sl l}}({\rm C}_{k;n})$ denote the threshold associated with idempotent-sum-free s…