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The Coefficients of Cyclotomic Polynomials

  • Helmut Maier
Chapter
Part of the Progress in Mathematics book series (PM, volume 85)

Abstract

Let \( {_n}(z) = \sum\nolimits_{m = o}^{(n)} {a(m,n){z^m}} \) be the nth cyclotomic polynomial. Let
$$ A\left( n \right)\, = \,\mathop {\max }\limits_{0\, \leqslant \,m\, \leqslant \,\phi \,\left( n \right)} \,\left| {a\,\left( {m,\,n} \right)} \right| $$
(1.1)
and let
$$ S\left( n \right)\, = \,\sum\limits_{0\, \leqslant \,m\, \leqslant \,\phi \,\left( n \right)\,} {\left| {a\,\left( {m,n} \right)} \right|} . $$
.

Keywords

Prime Factor Prime Divisor Chinese Remainder Theorem Asymptotic Density Prime Number Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    P. Bateman, C. Pomerance, and R. C. Vaughan, On the size of the ocefficients of the cyclotomic polynomial, Coll. Math. Soc. J. Bolyai (1981), 171–202.Google Scholar
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    N. G. de Bruijn, On the number of positive integers ≤ x and free of prime factors > y, Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951), 50–60.zbMATHGoogle Scholar
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    P.D.T.A. Elliott, Probabilistic Number Theory I, II, Springer-Verlag, New York, 1979/1980.Google Scholar
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    H. Halberstam, H.-E. Richert, Sieve Methods, Academic Press, London, 1974.zbMATHGoogle Scholar
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    H. Maier and G. Tenenbaum, On the set of divisors of an integer, Invent. Math. 76 (1984), 121–128.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Bikhäuser Boston 1990

Authors and Affiliations

  • Helmut Maier
    • 1
  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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