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The order of magnitude of the mth coefficients of cyclotomic polynomials

Published online by Cambridge University Press:  18 May 2009

H. L. Montgomery  and
R. C. Vaughan
H. L. Montgomery
Affiliation:
University of Michigan, Ann Arbor Michigan 48109, U.S.A.
R. C. Vaughan
Affiliation:
Imperial College, London
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We define the nth cyclotomic polynomial Φn(z) by the equation

and we write

where ϕ is Euler's function.

Erdös and Vaughan [3] have shown that

uniformly in n as m-→∞, where

and that for every large m

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 143 - 159
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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