Timeline for Distribution mod 1 of Factorial Multiples of Real Numbers.
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2010 at 11:38 | comment | added | Sidney Raffer | I like this - The problem is can one choose the $s_k$ so that $c$ is something familiar? And I wonder what are ALL POSSIBLE $c$'s defined in this way? | |
| Nov 11, 2010 at 11:09 | comment | added | Gerry Myerson | Maybe this works. Let $s_1,s_2,\dots$ be u.d. in $[0,1)$. Let $c=\sum[ks_k]/k!$. Then $\lbrace cn!\rbrace=t_{n+1}$ where $t_{n+1}-s_{n+1}$ goes to zero, so $\lbrace cn!\rbrace$ is u.d. in $[0,1)$. | |
| Nov 11, 2010 at 10:34 | comment | added | Sidney Raffer | Yes, This is Theorem 4.1 in Kuipers and Niederreiter. As you say the problems is to find an example. Maybe it is possible, to use some expression in $e$ to get an example that is dense mod 1? As for algebraic numbers $c$, could it be that we have no example where $cn!<1/2$ mod 1 infinitely often?! | |
| Nov 11, 2010 at 10:12 | history | answered | Gerry Myerson | CC BY-SA 2.5 |