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We estimate the distribution of relatively $r$-prime lattice points in numberfields $K$ with their components having a norm less than $x$. In the previouspaper we obtained uniform upper bounds as $K$ runs through all number fieldsunder assuming the Lindel\"of hypothesis. And we also showed unconditionalresults for abelian extensions with a degree less than or equal to $6$. In thispaper we remove all assumption about number fields and improve uniform upperbounds. Throughout this paper we consider estimates for distribution of idealsof the ring of integer $\mathcal{O}_K$ and obtain uniform upper bounds. Andwhen $K$ runs through cubic extension fields we show better uniform upperbounds than that under the Lindel\" of Hypothesis.

Uniform upper bounds of the distribution of relatively r-prime lattice points