Math Student
Reputation
Next privilege 250 Rep.
 Sep24 awarded Autobiographer Sep24 awarded Nice Question Apr11 awarded Nice Question Nov26 comment Determining the number of classes @KCd: I am learning this material. I know some ring theory and galois theory. i know that the group of classes is finite and abelian and also know minkowski's theorem. i think embedding this in a vector space and using properties of ideals there is a way to solve this but I need help. how would you do it? Nov25 asked Determining the number of classes Nov5 comment Equivalence to the prime number theorem @GerryMyerson: The edits seem to be exactly what I am looking for. Assuming $\sum_{n=1}^x\mu(n)=o(x)$ is fine, as I know how to prove that from PNT. Can you post the solution? I think such a solution is worth the bounty and acceptance. Google books doesn't give me the good section. Nov5 comment Equivalence to the prime number theorem @Phira: This is a good point, so I give you +1, but it is not exactly what I am looking for. Oct30 revised Equivalence to the prime number theorem deleted 12 characters in body Oct30 comment Equivalence to the prime number theorem I have put all my reputation for a bounty, and edited more. Oct30 awarded Promoter Oct30 revised Equivalence to the prime number theorem added 250 characters in body Oct30 revised Equivalence to the prime number theorem deleted 19 characters in body Oct29 awarded Critic Oct29 comment Equivalence to the prime number theorem I already know this, this is not my question. What you have shown is that $$\sum_{n\leq x} \frac{\Lambda(n)}{n} =\log x +O(1)$$ where the constant must be less then $2$. This is one of mertens estimates. What I want is significantly stronger, and that is $$\sum_{n\leq x} \frac{\Lambda(n)}{n} =\log x -\gamma +o(1).$$ This last estimate implies the prime number theorem, so you cannot hope to prove it without using something that strong. Oct29 revised Equivalence to the prime number theorem deleted 76 characters in body Oct29 comment Equivalence to the prime number theorem @anon: you are correct. Oct28 asked Equivalence to the prime number theorem Oct1 awarded Teacher Oct1 answered How to prove this inequality using prime number theorem Sep22 accepted The Cauchy-Crofton Formula