Timeline for Analytic continuation and convergence of a Riemann zeta related function
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 7, 2021 at 23:28 | vote | accept | Vincent Granville | ||
| May 7, 2021 at 23:08 | comment | added | GH from MO | @VincentGranville: The Wikipedia page defines the Dirichlet series for $\Re s>1$, because in that range we know convergence, and for $z=1$ you cannot replace $\Re s>1$ by $\Re s>0.999$, say. For $z=-1$ we conjecture that the Dirichlet series actually converges for $\Re s>1/2$: this is equivalent to the RH. | |
| May 7, 2021 at 22:32 | comment | added | Vincent Granville | I was talking about the third display in the section "Dirichlet Series" in the Wikipedia entry. It says that $|z|<2$ and $Re(s)>1$ (I assume for convergence) and here $z=-1$. But they could be wrong, they got the product wrong anyway I think; should be $1-z/p^s$, not $1+z/p^s$ in the product unless I am mistaken. I will redo my numerical computations anyway, because (unless some mistake), I could not get $L(0.9)$ to converge, but got $L^*(0.9)$ to converge to the correct value. | |
| May 7, 2021 at 21:23 | history | edited | GH from MO | CC BY-SA 4.0 | added 8 characters in body |
| May 7, 2021 at 21:18 | history | answered | GH from MO | CC BY-SA 4.0 |