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Ternary cyclotomic polynomials with an optimally large set of coefficients


Author: Gennady Bachman
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1943-1950
MSC (2000): Primary 11B83, 11C08
DOI: https://doi.org/10.1090/S0002-9939-04-07338-1
Published electronically: January 29, 2004
MathSciNet review: 2053964
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Abstract: Ternary cyclotomic polynomials are polynomials of the form $\Phi_{pqr}(z)=\prod_\rho(z-\rho)$, where $p<q<r$ are odd primes and the product is taken over all primitive $pqr$-th roots of unity $\rho$. We show that for every $p$ there exists an infinite family of polynomials $\Phi_{pqr}$ such that the set of coefficients of each of these polynomials coincides with the set of integers in the interval $[-(p-1)/2,(p+1)/2]$. It is known that no larger range is possible even if gaps in the range are permitted.


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Additional Information

Gennady Bachman
Affiliation: Department of Mathematical Sciences, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, Nevada 89154-4020
Email: bachman@unlv.nevada.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07338-1
Received by editor(s): July 13, 2002
Received by editor(s) in revised form: April 21, 2003
Published electronically: January 29, 2004
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2004 American Mathematical Society

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