All Questions

Update on 7/20/2020: It appears that conjecture A is not correct, you need more conditions for it to be true. See here (an answer to a previous MO question). The general problem that I try to solve is ...

Let $S$ be an infinite set of positive integers, $N_S(z)$ be the number of elements of $S$ less than or equal to $z$, and let $$D_S(z, n, p)= \sum_{k\in S,k\leq z}\chi(k\equiv p\bmod{n}).$$ Here $\chi$...