Let K/Q be a number field extention. Is there an asymptotic formular for the numer of ideals $\sum\limits_{\substack{N(A)\leq x\\N(A)\equiv k(q)}}1$,where $(k,q)=1$ and $A$ runs over ideals in $O_K$. If there was, where to find.
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2$\begingroup$ Welcome to MO! I think it would be a good idea to provide more details and a motivation for your question. $\endgroup$– UwFCommented Mar 17, 2014 at 14:11
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4$\begingroup$ I second UwF. You should edit your question and precise at least in what rings are taken your ideals (presumably the ring of integers of a number fields) and what you mean by arithmetic progression in this context. $\endgroup$– JoëlCommented Mar 17, 2014 at 16:05
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$\begingroup$ Dear Kui Liu, I think such a formula can be obtained by the methods of Lang, Algebraic Number Theory, chapter 6, section 3. Did you know this reference? $\endgroup$– JoëlCommented Mar 18, 2014 at 13:36
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$\begingroup$ Dear Joël,thank you very much. I know that reference, but I am not familiar with the adele language of that book. Is the method there similar to the method in this paper? sciencedirect.com/science/article/pii/S0723086906000375 $\endgroup$– Kui LiuCommented Mar 19, 2014 at 2:01
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