Timeline for A Sequence of Real numbers
Current License: CC BY-SA 3.0
11 events
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| Sep 13, 2013 at 15:11 | vote | accept | CommunityBot | ||
| Jun 21, 2013 at 20:37 | comment | added | Dietrich Burde | @Peter: thank you. This is important to know. | |
| Jun 21, 2013 at 20:36 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Jun 21, 2013 at 20:24 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Jun 21, 2013 at 17:33 | comment | added | Stefan Kohl♦ | By the way, Carella acknowledges in his paper Hugh Montgomery for "comments and correcting a few errors". Don't know whether Montgomery has ever seen the paper, though ... . | |
| Jun 21, 2013 at 17:13 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Jun 21, 2013 at 16:52 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Jun 21, 2013 at 15:49 | vote | accept | CommunityBot | ||
| Jun 21, 2013 at 20:20 | |||||
| Jun 21, 2013 at 15:42 | comment | added | Peter Humphries | Unfortunately Carella is a well-known crank, and the claimed error term is false. In fact, Montgomery proved that the error term $H(x)$ satisfies $H(x)=\Omega(\sqrt{\log\log x})$. On the other hand, Walfisz proved that $H(x)=O((\log x)^{2/3}(\log\log x)^{4/3}))$. Actually in both cases these bounds were for the error term $R(x)=\sum_{n\le x}{\varphi(n)}-\frac{3x^2}{\pi^2}$, and then both results follow from a result of Chowla showing that $H(x)-\frac{R(x)}{x}=O((\log x)^{-4})$; see mathoverflow.net/questions/126890/…. | |
| Jun 21, 2013 at 13:33 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Jun 21, 2013 at 9:42 | history | answered | Dietrich Burde | CC BY-SA 3.0 |