Timeline for Prime factor distribution over $\mathbb{N}$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 17, 2021 at 5:47 | vote | accept | Raphael J.F. Berger | ||
| Jul 16, 2021 at 22:11 | comment | added | Will Sawin | @RaphaelJ.F.Berger Actually I expect the function will behave like $f_n(x) = \begin{cases} 0 & x\leq0 \\ nx & 0 \leq x \leq 1/n \\ 2-nx & 1/n \leq x \leq 2/n \\ 0 & x \geq 2/n \end{cases}$ which pointwise converges to $0$ everywhere but has integral $1$. | |
| Jul 16, 2021 at 22:08 | comment | added | Raphael J.F. Berger | The other alternative would be to divide the intervalls simply in $k$ pieces, such that all functions have $\delta(1)\ne0$ in that case it's immediately clear that it will converge to constant $1$ since all "combinations exist". | |
| Jul 16, 2021 at 22:03 | comment | added | Raphael J.F. Berger | Very nice - thank you very much! I suppose then it will have poles at $\frac{1}{d}$? Can we say anything on the order of these poles? After all the integral has to be $1$ as well, in this case, I suppose. | |
| Jul 16, 2021 at 21:56 | history | answered | Will Sawin | CC BY-SA 4.0 |