I know that the Prime Number Theorem gives us that $$ \sum_{ p \leq n}\frac{1}{p} \sim \log{\log{n}} $$ as seen in "An introduction to the Theory of Numbers ", by Hardy and Wright and would like to know how does one get that for a quadratic character $ \chi $ mod $ n $ we have that $$ \sum_{ p \leq n,\chi(p)=1}\frac{1}{p} \sim \frac{1}{\varphi(n)}\log{\log{n}} $$

I appreciate any help and comments! Thank you!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.