Is this special case known? For $\lambda(q)$ -- well-factorable function and $q|P(z)$, $\pi(x;q,a)$ $a=1$. $\displaystyle \sum_{q\leq x^{1-\epsilon}} \lambda(q) ( \pi (x;q,1)-\frac{\pi(x)}{\varphi (q)} )\leq \frac{Cx}{\log^A(x) }$
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1$\begingroup$ You should edit your old question mathoverflow.net/questions/356043/… and ask for it to be reopened, rather than starting a new post $\endgroup$– Yemon ChoiCommented Mar 30, 2020 at 4:30
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$\begingroup$ I do not know how. $\endgroup$– user155294Commented Mar 30, 2020 at 4:34
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$\begingroup$ When you go to your old question, do you see any options for editing? Perhaps you may need to register as a user first, a move which I would strongly recommend since it prevents the proliferation of multiple user accounts and duplicate questions $\endgroup$– Yemon ChoiCommented Mar 30, 2020 at 4:36
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2$\begingroup$ Does this answer your question? Primes in arithmetic progression $\endgroup$– JRNCommented Mar 30, 2020 at 6:36
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1$\begingroup$ What is a well-factorable function? What is $P(z)$? $\endgroup$– WojowuCommented Mar 30, 2020 at 14:31
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1 Answer
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This type was proved by Bombieri, Friedlander and Iwaniec in the paper "Primes in arithmetic progressions to large moduli.
