Timeline for Mahler measure of a totally positive, expanding algebraic integer
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2023 at 8:01 | comment | added | Kalas678 | Got it. Holder gives, $a \geq 2 \sqrt{a-1}$. | |
| Dec 26, 2023 at 20:25 | comment | added | Kalas678 | Which version of Holder's inequality you are using here? @XiaoshengMu | |
| Apr 22, 2016 at 4:44 | answer | added | Xiaosheng Mu | timeline score: 3 | |
| Apr 22, 2016 at 4:19 | comment | added | Fan Zheng | @BobbyGrizzard NOT the OP LOL | |
| Apr 22, 2016 at 3:19 | vote | accept | Xiaosheng Mu | ||
| Apr 21, 2016 at 11:58 | comment | added | Bobby Grizzard | @FanZheng yes. Here is one effective result: ams.org/journals/mcom/1996-65-213/S0025-5718-96-00664-3/… edit: and here is the one I was probably looking at yesterday, due to Wu and Mu (Quanwu Mu, not the OP!): sciencedirect.com/science/article/pii/S0022314X12001989 | |
| Apr 21, 2016 at 5:50 | comment | added | Fan Zheng | @BobbyGrizzard Is the "with finitely many exceptions" part effective? | |
| Apr 20, 2016 at 22:58 | comment | added | Gerry Myerson | On the hypothesis that $\alpha$ is algebraic of degree $d$, the value $\alpha=2$ can only arise in the case $d=1$, so the equality $N(\alpha)=2^d$ is achieved only for $d=1$, $\alpha=2$. | |
| Apr 20, 2016 at 22:53 | answer | added | Gypsum | timeline score: 5 | |
| S Apr 20, 2016 at 21:37 | history | suggested | Bobby Grizzard |
added some tags
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| Apr 20, 2016 at 21:15 | review | Suggested edits | |||
| S Apr 20, 2016 at 21:37 | |||||
| Apr 20, 2016 at 21:13 | comment | added | Bobby Grizzard | Interesting question. I assume you're familiar with work of Smyth, Flammang, etc. on lower bounds for the Mahler measure of totally positive algebraic integers? (These give a lower bound of $C=1.722...$ for $M(\alpha)^{1/d}$ with finitely many exceptions, but valid for all totally positive integers $\alpha$, not just those with all conjugates $>1$). | |
| Apr 20, 2016 at 20:40 | review | First posts | |||
| Apr 20, 2016 at 21:32 | |||||
| Apr 20, 2016 at 20:35 | history | asked | Xiaosheng Mu | CC BY-SA 3.0 |