3 problems

For a prime $q$, let $n(q)$ denote the least natural number that is not a quadratic residue modulo $q$. Vinogradov's conjecture. For every fixed $\varepsilon>0$, … This conjecture…

Let $f$ be a random completely multiplicative function taking values in $\\{1,-1\\}$, with the values $f(p)$ chosen independently and uniformly at random over the primes. Let…

Let $p$ be a prime, and let $n_p$ denote the least positive quadratic nonresidue modulo $p$. Here $f(p)\ll g(p)$ means that there is a constant $C>0$ such that $f(p)\leq Cg(p)$ for…