Timeline for Contour integration of $\zeta(s)\zeta(2s)$
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2011 at 3:58 | comment | added | David Hansen | Sorry, $h(x)$ is $1$ if $x<1$, $1/2$ if $x=1$, and $0$ if $x>1$. | |
| Mar 17, 2011 at 3:57 | comment | added | David Hansen |
Try using the approximate Perron formula $h(x)=\frac{1}{2\pi i} \int_{\sigma -iT}^{\sigma + iT}x^s \frac{ds}{s}+O(T^{-1}x^{\sigma})$ and the convexity bound for the zeta function.
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| Mar 17, 2011 at 2:28 | comment | added | AbelianGrapes | I'm still trying to solve this using perron's formula. I am using cauchy's theorm for c=3/4 but I'm having some trouble bounding this integral. | |
| Mar 16, 2011 at 15:43 | comment | added | GH from MO | @unknown: The sum of coefficients of $\prod_{k=1}^K\zeta(ks)$ up to $X$ is $x\prod_{k=2}^K\zeta(k)+O_K(\sqrt{x})$. This can be seen by induction on $K$, using a similar calculation as the response above. | |
| Mar 16, 2011 at 5:09 | comment | added | AbelianGrapes | Thank you. If anyone knows how to extend this to $\Pi\zeta(ks)$ it would be very much appreciated | |
| Mar 16, 2011 at 3:19 | vote | accept | AbelianGrapes | ||
| Mar 16, 2011 at 3:10 | history | answered | David Hansen | CC BY-SA 2.5 |