4 problems

Let $\mathcal{M}$ denote the class of multiplicative functions under consideration, and let $f_1,\ldots,f_k\in\mathcal{M}$. Suppose that for some $1\leq j_0\leq k$, the function…

Logarithmically averaged Chowla conjecture. These correlations tend to zero as $N\to\infty$:

Let $x\geq 1$, let $h$ be an integer with $1\leq h\leq x^{1-\varepsilon}$, and let $\varepsilon>0$. Let $C(h)$ be a constant depending only on $h$. Squarefree correlation conjectur…

Let $\alpha,\beta,\gamma,\delta$ be complex parameters, let $h$ be a positive integer, and define $I_{\alpha,\gamma}(n)=\sum_{de=n}\mu(e)d^{-\alpha}e^{-\gamma}$. Let $r_q(h)$ and…