Timeline for Intuition behind the Riemann $\zeta$ functional equation
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2017 at 3:07 | comment | added | reuns | @Lucian See this proof (Démonstration) $\zeta(s) = \chi(s) \zeta(1-s)$ where $\chi(s) = \frac{s}{\pi} \int_0^\infty x^{-s-1} \sin(\pi x)dx$ | |
| Apr 20, 2017 at 18:31 | comment | added | Lucian | $\dfrac{\zeta(1-s)}{2^{1-s}}=\Gamma(s)\cos\left(\dfrac\pi2s\right)\dfrac{\zeta(s)}{\pi^s}$ has a certain niceness to it, but leaves the exponential factor on the left unexplained. Perhaps an influence of the Dirichlet $\eta$ function, which helps expand Riemann's $\zeta$ on $(0,1)$ ? | |
| Apr 20, 2017 at 18:03 | history | answered | Myshkin | CC BY-SA 3.0 |