On the correlation measures of subsets based on multiplicative and additive characters

Dartyge and S\'ark"ozy constructed pseudorandom subsets based on the argument of multiplicative characters $\chi$ and additive characters $\psi$, and gave good estimates for the case $\psi$ being non-trivial. This paper further studies the pseudorandom properties of subsets based on $\chi$ and $\psi$, and proves sharp estimates of pseudorandom measures for all non-trivial characters $\chi$ of order $w$.