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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.

flag	asked Aug 2 2010 at 9:52 Chandrasekhar 2,010●1●11●27

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 2010 at 10:01

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Oh! No please dont end my curiosity by closing this thread. – Chandrasekhar Aug 2 2010 at 10:11

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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 2010 at 10:45

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Please make some effort to solve your own curiosity questions. – Tsuyoshi Ito Aug 3 2010 at 11:45

Charles Matthews · Accepted Answer · 2010-08-02 10:30:53Z UTC

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

answered Aug 2 2010 at 10:30

Charles Matthews
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Hashem sazegar · Answer 2 · 2010-08-03 11:24:26Z UTC

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

answered Aug 3 2010 at 11:24

Hashem sazegar
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Dirichlet’s Divisor Function

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