Geodesic
The order of magnitude of the mth coefficients of cyclotomic polynomials
Glasgow mathematical journal, Tome 26 (1985), pp. 143-159

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

We define the nth cyclotomic polynomial Φn(z) by the equationand we writewhere φ is Euler's function.Erdös and Vaughan [3] have shown thatuniformly in n as m-→∞, whereand that for every large m 
Montgomery, H. L.; Vaughan, R. C. The order of magnitude of the mth coefficients of cyclotomic polynomials. Glasgow mathematical journal, Tome 26 (1985), pp. 143-159. doi: 10.1017/S0017089500006145
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[1] 1.Davenport, H., On some infinite series involving arithmetical functions II, Quart. J. Math Oxford, 8 (1937), 313–320. Google Scholar | DOI

[2] 2.Davenport, H., Multiplicative number theory, Second Edition, revised by Montgomery, H. L., (Springer-Verlag 1980). Google Scholar | DOI

[3] 3.Erdös, P., and Vaughan, R. C., Bounds for the r-th coefficients of cyclotomic polynomials, J. London Math. Soc. (2) 8 (1974), 393–400. Google Scholar | DOI

[4] 4.Halberstam, H., and Richert, H.-E., Sieve methods, (Academic Press, London, 1974). Google Scholar

[5] 5.Landau, Edmund, Vorlesungen über Zahlentheorie, (Chelsea, New York, 1955). Google Scholar

[6] 6.Montgomery, H. L. and Vaughan, R. C., Exponential sums with multiplicative coefficients, Invent. Math. 43 (1977), 69–82. Google Scholar | DOI

[7] 7.Titchmarsh, E. C., The theory of the Riemann zeta function, (Clarendon Press, Oxford, 1951). Google Scholar

[8] 8.Vaughan, R. C., Bounds for the coefficients of cyclotomic polynomials, Michigan Math J. 21 1974), 289–295. Google Scholar

[9] 9.Vaughan, R. C., The Hardy–Littlewood method, (Cambridge University Press, 1981). Google Scholar

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