Advertisement

The multiplicities of qth root number functions

  • Stefan-C. VirchowEmail author
Article
  • 16 Downloads

Abstract

We consider the qth root number function for the symmetric group. Our aim is to develop an asymptotic formula for the multiplicities of the qth root number function as q tends to \(\infty \). We use character theory, number theory, and combinatorics.

Keywords

Symmetric group qth Root number function Multiplicities Character theory 

Mathematics Subject Classification

20B30 20C15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics. Addison-Wesley, Reading (1991)zbMATHGoogle Scholar
  2. 2.
    Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. Clarendon, Oxford (1954)zbMATHGoogle Scholar
  3. 3.
    Kerber, A.: Algebraic Combinatorics via Finite Group Actions. BI-Wissenschaftsverlag, Mannheim (1991)zbMATHGoogle Scholar
  4. 4.
    Moll, V.H.: Numbers and Functions. AMS, Providence (2012)zbMATHGoogle Scholar
  5. 5.
    Müller, T.W., Schlage-Puchta, J.-C.: Character theory of symmetric groups, subgroup growth of Fuchsian groups, and random walks. Adv. Math. 213, 919–982 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Sagan, B.E.: The Symmetric Group. Springer, New York (2001)CrossRefGoogle Scholar
  7. 7.
    Scharf, T.: Die Wurzelanzahlfunktion in symmetrischen Gruppen. J. Algebra 139, 446–457 (1991)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institut für MathematikUniversität RostockRostockGermany

Personalised recommendations