WHAT IS Lehmer's number?

• Published in 2009
• Added on 2013-12-03

Lehmer's number \(\lambda \approx 1.17628\) is the largest real root of the polynomial \(f_\lambda(x) = x^{10} + x^9 - x^7 - x^6 -x^5 -x^4 - x^3 + x + 1\). This number appears in various contexts in number theory and topology as the (sometimes conjectural) answer to natural questions involving ``minimality'' and ``small complexity''.

Links

• http://www.math.fsu.edu/~aluffi/archive/paper355.pdf

Other information

BibTeX entry

@article{item35,
	key = {item35},
	type = {article},
	title = {WHAT IS Lehmer's number?},
	author = {Eriko Hironaka},
	abstract = {Lehmer's number \(\lambda \approx 1.17628\) is the largest real root of the polynomial \(f{\_}\lambda(x) = x^{\{}10{\}} + x^9 - x^7 - x^6 -x^5 -x^4 - x^3 + x + 1\).

This number appears in various contexts in number theory and topology as the (sometimes conjectural) answer to natural questions involving ``minimality'' and ``small complexity''.},
	comment = {},
	date_added = {2013-12-03},
	date_published = {2009-12-07},
	urls = {http://www.math.fsu.edu/{\~{}}aluffi/archive/paper355.pdf},
	collections = {attention-grabbing-titles,integerology},
	url = {http://www.math.fsu.edu/{\~{}}aluffi/archive/paper355.pdf},
	urldate = {2013-12-03},
	year = 2009
}