Consequences of the Continuity of the Monic Integer Transfinite Diameter
| dc.creator | Hilmar, Jan | |
| dc.date | 2007-03-29 | |
| dc.date | 2007-06-06 | |
| dc.date.accessioned | 2026-07-07T08:04:15Z | |
| dc.date.available | 2026-07-07T08:04:15Z | |
| dc.description | We consider the problem of determining the monic integer transfinite diameter for real intervals $I$ of length less than 4. We show that $t_M([0,x])$, as a function in $x>0$, is continuous, therefore disproving two conjectures due to Hare and Smyth. Consequently, for $n>2\in\naturals$, we define the quantity $b_{\max}(n)&=&\sup_{b>\frac{1}{n}}\left\{b|t_M([0,b])=\tfrac{1}{n}\right.\right\}$ and give lower and upper bounds of $b_{\max}(n)$. Finally, we improve the lower bound for $b_{\max}(n)$ for $3\leq n\leq 8$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703888 | |
| dc.identifier | http://arxiv.org/abs/math/0703888 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129887 | |
| dc.subject | Number Theory | |
| dc.title | Consequences of the Continuity of the Monic Integer Transfinite Diameter | |
| dc.type | text |