Consequences of the Continuity of the Monic Integer Transfinite Diameter

Details Consequences of the Continuity of the Monic Integer Transfinite Diameter Consequences of the Continuity of the Monic Integer Transfinite Diameter

2007-03-29

arxiv.org/abs/math/0703888v3

Mathematics

Number Theory

11 pages

Scientific paper

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 $3\leq n\leq 8$.

Affiliated with

Also associated with

No associations

Rating

Consequences of the Continuity of the Monic Integer Transfinite Diameter does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Consequences of the Continuity of the Monic Integer Transfinite Diameter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Consequences of the Continuity of the Monic Integer Transfinite Diameter will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-711276