Weak approximation for number fields
= Weak approximation for number fields
Given finitely many distinct <places of a number field> $v_1,\ldots,v_r$, the diagonal image of $K$ is dense in $\prod_i K_{v_i}$. One can therefore simultaneously prescribe finite congruences and real signs. This is useful in the <ray class exact sequence> and in finding representatives of an <ideal class> prime to a prescribed finite set of <prime ideals>.