Interesting Esoterica

WHAT IS Lehmer's number?

Article by Eriko Hironaka
  • Published in 2009
  • Added on
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''.

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BibTeX entry

@article{item35,
	title = {WHAT IS Lehmer's number?},
	author = {Eriko Hironaka},
	url = {http://www.math.fsu.edu/{\~{}}aluffi/archive/paper355.pdf},
	urldate = {2013-12-03},
	year = 2009,
	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 = {},
	collections = {Attention-grabbing titles,Integerology}
}