Timeline for On a certain inverse Mellin transform involving $\zeta$
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| May 8, 2021 at 13:01 | comment | added | reuns | Did you investigate the convergence? Once you know that for $c >2$, $\frac{1}{2\pi i}\lim_{T\to \infty} \int_{c-iT}^{c+iT} \frac{\zeta(s-1)}{s}x^s ds=\sum_{n\le x} n$ then apply the residue theorem to $\lim_{a\to 0^+} \frac{1}{2\pi i} \int_{(c)} e^{a(s-c)^2} \frac{\zeta(s-1)}{s}x^s ds$ to obtain $f(1/x)=\sum_{n\le x} n-\frac{x^2}2$ at least in the sense of distributions. | |
| May 8, 2021 at 12:18 | comment | added | Carlo Beenakker | if $\zeta(s-1)$ is replaced by $\zeta(s)$ this equals the integer part of $x$ --- math.stackexchange.com/q/751948/87355 | |
| May 8, 2021 at 11:58 | history | asked | Ofir Gorodetsky | CC BY-SA 4.0 |