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- Title
Notes on the Borwein-Choi conjecture of Littlewood cyclotomic polynomials.
- Authors
Shao Fang Hong; Wei Cao
- Abstract
Borwein and Choi conjectured that a polynomial P( x) with coefficients ±1 of degree N − 1 is cyclotomic iff , where N = p 1 p 2 ... p r and the p i are primes, not necessarily distinct. Here Φ p ( x):= ( x p − 1)/( x − 1) is the p-th cyclotomic polynomial. They also proved the conjecture for N odd or a power of 2. In this paper we introduce a so-called E-transformation, by which we prove the conjecture for a wider variety of cases and present the key as well as a new approach to investigate the conjecture.
- Subjects
POLYNOMIALS; APPROXIMATION theory; ALGEBRA; CYCLOTOMIC fields; FIELD extensions (Mathematics); ALGEBRAIC fields
- Publication
Acta Mathematica Sinica, 2009, Vol 25, Issue 1, p65
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-008-6444-5