4 problems

Fix an integer $a\ne0$, positive integers $\nu_1,\ldots,\nu_s$, and integers $h_s>\cdots>h_1\geqslant0$. Let ${\mathcal K}_m^*(a)$ be the normalized Kloosterman-sum quantity and le…

Let $\lambda$ be the Liouville function. For every $t\in\mathbb{N}$ and every collection of distinct natural numbers $h_1,\ldots,h_t$, logarithmic Chowla conjecture. One has … This…

Let $f\in\mathbb{Z}[x_1,\ldots,x_h]$ be a primitive squarefree polynomial, let $\mathcal{A}$ be an arithmetic progression, and let $\mathcal{A}(X)$ denote its points of norm at mos…

Let $k\geq 1$, let $a_1,\dots,a_k$ be natural numbers, and let $b_1,\dots,b_k$ be distinct nonnegative integers satisfying … for $1\leq i<j\leq k$. Let $\lambda$ denote the Liouvil…