Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

We know that by Dirichlet's formula for the Divisor function $ \displaystyle \sum\limits_{n \leq x} d(n) = x \log{x} + (2C-1)x + \mathcal{O}(\sqrt{x})$.

What is the best approximation available till date for the given formula. I know that finding the infimum of the $\mathcal{O}'s$ is an unsolved problem, but would like to see the closest approximation.

share|improve this question
This question was already asked on MO, I'll try to find it (and close yours afterwards :-( ). You are very-very curious! :-) –  Wadim Zudilin Aug 2 '10 at 10:01
Oh! No please dont end my curiosity by closing this thread. –  Chandrasekhar Aug 2 '10 at 10:11
I don't know why should it stay open in this wrong form. ;-) BTW, all question lovers are advised to first visit the OEIS and Wikipedia, before posting their questions. You obviously missed this standard procedure... –  Wadim Zudilin Aug 2 '10 at 10:45
Please make some effort to solve your own curiosity questions. –  Tsuyoshi Ito Aug 3 '10 at 11:45
add comment

2 Answers

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.