5 problems

Mean-value formula conjecture. The mean value is equal to

Let $x$ be sufficiently large. Consider a real-valued completely multiplicative function $f$ satisfying $|f(n)|\leq 1$ for every positive integer $n$, and suppose that $f(p)=0$ for…

Square mean Lindelöf hypothesis. The value $\eta=0$ is admissible.

Koyama's mean Lindelöf hypothesis. The displayed bound should hold.

Let $X$ be sufficiently large, and let ${\mathbf f}=(f_1,\ldots,f_t)$ be a well-conditioned $t$-tuple of polynomials with integral coefficients, where $\deg(f_j)=k_j$. Define … whe…