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 , where are odd primes and the product is taken over all primitive -th roots of unity . We show that for every there exists an infinite family of polynomials such that the set of coefficients of each of these polynomials coincides with the set of integers in the interval . 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