Geodesic
A Generalization of the Cyclotomic Polynomial
Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 461-466

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Rao, K. Nageswara. A Generalization of the Cyclotomic Polynomial. Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 461-466. doi: 10.4153/CMB-1976-069-8
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[1] 1. Apostol, Tom M., The resultant of the cyclotomic polynomials F(ax) and F(bx). Math. Comp. 29 (1975), 1–6. Google Scholar

[2] 2. Cohen, Eckford, A class of arithmetical functions. Proc. Nat. Acad. Sci. USA, 41 (1955), 939–944. Google Scholar

[3] 3. McCarthy, Paul J., Regular arithmetical convolutions. Port. Math. 27 (1968), 1–13. Google Scholar

[4] 4. McCarthy, Paul J., Arithmetical functions and distributivity. Canad. Math. Bull. 13 (1970), 491–496. Google Scholar

[5] 5. McCarthy, Paul J., Regular arithmetical convolutions and the solution of linear congruences. Colloq. Math 22 (1971), 215–222. Google Scholar

[6] 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] 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] 8. Nageswara Rao, K., On a congruence equation and related arithmetical identities. Monatsh. Math. 71 (1967), 24–31. Google Scholar

[9] 9. Narkiewicz, W., On a class of arithmetical convolutions. Colloq. Math. 10 (1963), 81–94. Google Scholar

[10] 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

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