Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-14T19:04:12.106Z Has data issue: false hasContentIssue false
  • English
  • Français

A Generalization of the Cyclotomic Polynomial

Published online by Cambridge University Press:  20 November 2018

K. Nageswara Rao
K. Nageswara Rao*
Affiliation:
Dept. of Mathematics, North Dakota State UniversityFargo, North Dakota 58102, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, the cyclotomic polynomial is generalized and several of its properties based on the Môbius inversion are derived. It is deduced that a polynomial whose roots are the roots of a cyclotomic polynomial multiplied by those of another cyclotomic polynomial is the product of cyclotomic polynomials. Character sums and finite Fourier series are employed for the latter result.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 461 - 466
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Apostol, Tom M., The resultant of the cyclotomic polynomials Fm(ax) and Fn(bx). Math. Comp. 29 (1975), 1–6.Google Scholar
2. Cohen, Eckford, A class of arithmetical functions. Proc. Nat. Acad. Sci. USA, 41 (1955), 939–944.Google Scholar
3. McCarthy, Paul J., Regular arithmetical convolutions. Port. Math. 27 (1968), 1–13.Google Scholar
4. McCarthy, Paul J., Arithmetical functions and distributivity. Canad. Math. Bull. 13 (1970), 491–496.Google Scholar
5. McCarthy, Paul J., Regular arithmetical convolutions and the solution of linear congruences. Colloq. Math 22 (1971), 215–222.Google Scholar
6. Menon, P. K., On Vaidyanathaswamy’s class division of the residue classes modulo N. J. Indian Math. Soc. 26 (1962), 167–186.Google Scholar
7. Nageswara Rao, K., Unitary class division of integers mod n and related arithmetical identities. J. Indian Math. Soc. 30 (1966), 195–205.Google Scholar
8. Nageswara Rao, K., On a congruence equation and related arithmetical identities. Monatsh. Math. 71 (1967), 24–31.Google Scholar
9. Narkiewicz, W., On a class of arithmetical convolutions. Colloq. Math. 10 (1963), 81–94.Google Scholar
10. Vaidyanathaswamy, R., A remarkable property of integers modN and its bearing on group theory. Proc. Ind. Acad. Sci. 5A (1937), 63–75.Google Scholar