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visits member for 3 years, 8 months
seen Nov 26 '11 at 21:21

I am a Math Student. I do take courses, but mainly learn on my own. I like Algebra most, but am curious about number theory. These questions cause me problems as I am not too strong there.


Sep
24
awarded  Autobiographer
Sep
24
awarded  Nice Question
Apr
11
awarded  Nice Question
Nov
26
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?
Nov
25
asked Determining the number of classes
Nov
5
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.
Nov
5
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.
Oct
30
revised Equivalence to the prime number theorem
deleted 12 characters in body
Oct
30
comment Equivalence to the prime number theorem
I have put all my reputation for a bounty, and edited more.
Oct
30
awarded  Promoter
Oct
30
revised Equivalence to the prime number theorem
added 250 characters in body
Oct
30
revised Equivalence to the prime number theorem
deleted 19 characters in body
Oct
29
awarded  Critic
Oct
29
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.
Oct
29
revised Equivalence to the prime number theorem
deleted 76 characters in body
Oct
29
comment Equivalence to the prime number theorem
@anon: you are correct.
Oct
28
asked Equivalence to the prime number theorem
Oct
1
awarded  Teacher
Oct
1
answered How to prove this inequality using prime number theorem
Sep
22
accepted The Cauchy-Crofton Formula