Timeline for Proof of equidistribution theorem for exponential coefficients
Current License: CC BY-SA 3.0
9 events
when toggle format | what | by | license | comment | |
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Jul 18, 2014 at 23:01 | vote | accept | jgonagle | ||
Jul 18, 2014 at 8:39 | answer | added | Kurisuto Asutora | timeline score: 3 | |
Jul 18, 2014 at 3:55 | comment | added | so-called friend Don | Asking that $\{2^n \alpha\}_{n \ge 1}$ be equidistributed mod $1$ is exactly equivalent to asking that $\alpha$ be normal in base $2$. Not a single irrational algebraic number is known to be $2$-normal; for some partial results, see this paper of Bailey, Borwein, Crandall, and Pomerance: crd.lbl.gov/~dhbailey/dhbpapers/algebraic.pdf | |
Jul 17, 2014 at 23:39 | comment | added | Gerry Myerson | Theorem 4.1 of Kuipers & Niederreiter says that if $a_1,a_2,\dots$ is any sequence of distinct integers then the sequence $a_1x,a_2x,\dots$ is uniformly distributed mod 1 for almost all real $x$. Of course this says nothing about any particular $x$, nor about the set of algebraic $x$, as that set has measure zero. The Theorem is due to Weyl, and it's noted that the case $a_n=b^n$, $b\ge2$ an integer, was studied by Hardy & Littlewood in 1914. | |
Jul 17, 2014 at 21:58 | history | edited | jgonagle | CC BY-SA 3.0 |
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Jul 17, 2014 at 21:50 | history | edited | jgonagle | CC BY-SA 3.0 |
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Jul 17, 2014 at 21:37 | vote | accept | jgonagle | ||
Jul 17, 2014 at 21:42 | |||||
Jul 17, 2014 at 21:11 | answer | added | GH from MO | timeline score: 7 | |
Jul 17, 2014 at 20:50 | history | asked | jgonagle | CC BY-SA 3.0 |