3 problems

Fujii's conjecture. For every $\alpha>0$, replacing $e^{-p/x}$ by $e^{-(p/x)^\alpha}$ gives a statement equivalent to the Generalized Riemann Hypothesis for $L(s,\chi_4)$; likewise…

Fix $k\geqslant 3$, and consider numbers composed of exactly $k$ prime factors, namely numbers $p_1^{a_1}\cdots p_j^{a_j}$ with $a_1+\cdots+a_j=k$, distributed in arithmetic progre…

Let $q$ be a modulus, and let $a$ and $b$ be reduced residue classes modulo $q$, with $a$ a quadratic non-residue and $b$ a quadratic residue. For the counting function of products…