-3
$\begingroup$

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.

$\endgroup$
3
  • $\begingroup$ This question was already asked on MO, I'll try to find it (and close yours afterwards :-( ). You are very-very curious! :-) $\endgroup$ Aug 2, 2010 at 10:01
  • 2
    $\begingroup$ 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... $\endgroup$ Aug 2, 2010 at 10:45
  • 2
    $\begingroup$ Please make some effort to solve your own curiosity questions. $\endgroup$ Aug 3, 2010 at 11:45

2 Answers 2

4
$\begingroup$

Use Wikipedia: http://en.wikipedia.org/wiki/Dirichlet_divisor_problem .

$\endgroup$
2
$\begingroup$

you can see also this paper:http://hkumath.hku.hk/~imr/IMRPreprintSeries/2010/IMR2010-10.pdf

$\endgroup$

Your Answer

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

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