On Landau’s Function g(n)

Jean-Louis Nicolas ()
Additional contact information
Jean-Louis Nicolas: Université de Lyon, CNRS, Institut Camille Jordan, Mathématiques

A chapter in The Mathematics of Paul Erdős I, 2013, pp 207-220 from Springer

Abstract: Abstract Let S n be the symmetric group of n letters. Landau considered the function g(n) defined as the maximal order of an element of S n ; Landau observed that (cf. [9]) 1 $$\displaystyle{ g(n) =\max \mathrm{lcm}(m_{1},\ldots,m_{k}) }$$ where the maximum is taken on all the partitions $$n = m_{1} + m_{2} + \cdots + m_{k}$$ of n and proved that, when n tends to infinity 2 $$\displaystyle{ \log g(n) \sim \sqrt{n\log n}. }$$ More precise asymptotic estimates have been given in [11, 22, 25].

Keywords: Precise Asymptotic Estimates; Symmetric Group; Maximum Order; Twin Prime Conjecture; Ramanujan (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_14

Ordering information: This item can be ordered from
http://www.springer.com/9781461472582

DOI: 10.1007/978-1-4614-7258-2_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().