Timeline for On partial sum estimate on the series $S(p,q;s)=\sum_1^q\frac{\sin^2(\frac{p\Gamma(n)}{n})}{n^s}$ and other Generalizations
Current License: CC BY-SA 4.0
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| Feb 24, 2020 at 20:20 | comment | added | Carlo Beenakker | OK, this was not clear at all to me from the question, apologies, the estimate I gave in this answer applies to generic values of $p$; so you want to be able to estimate something like $\sum_{k=\text{prime}}k^{-s}\cos^2(\pi/2k)$. | |
| Feb 24, 2020 at 20:14 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 24, 2020 at 20:03 | comment | added | bambi | thank you for the answer. But, the main purpose of the question is very different . See for ex . for $p=\pi/2$ the $\sin²$ term is finite for primes and zero for non prime . So I mentioned 'sharp' for this purpose . I need critical details of $I_2$. (The sum is very delicate for such critical values )I'm just following the advice of F.R.Villegas to generalize the series with such parametrization | |
| Feb 24, 2020 at 20:01 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 24, 2020 at 19:56 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 24, 2020 at 19:43 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |