Inverse cyclotomic polynomials |
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Authors: | Pieter Moree |
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Institution: | Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany |
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Abstract: | Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x)=(xn−1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n<561 all coefficients of Ψn(x) are ?1 in absolute value. We establish various properties of the coefficients of Ψn(x), especially focusing on the easiest non-trivial case where n is composed of 3 distinct odd primes. |
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Keywords: | 11B83 11C08 |
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