4 problems

Pure reversed-prime asymptotic conjecture. For every $A>0$,

Let $b\geq 2$ be fixed. Define … and … Also let $\#\mathfrak{B}(N)$ denote the number of admissible integer representations encoded by the source's set $\mathfrak{B}(N)$. Asymptoti…

Davenport's geometric-condition conjecture. If $C$ satisfies Davenport's Geometric Condition, then the asymptotic formula for the number of solutions to $C(\mathbf{x})=0$ holds wit…

For $N\in\mathbb{N}$, let $\mathbb{S}^1_+(N)$ be the upper semicircle of radius $\sqrt N$, and let $S_N=\mathbb{S}^1_+(N)\cap\mathbb{Z}^2$. Cilleruelo–Granville conjecture. For eve…