In mathematics, more specifically in algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with… (More)

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2012

2012

We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.

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2008

2008

- Yves Gallot, Pieter Moree, Huib Hommersom
- 2008

Let an(k) be the kth coefficient of the nth cyclotomic polynomial Φn(x). As n ranges over the integers, an(k) assumes only… (More)

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2008

2008

- Yimin Ge
- 2008

Abstract Elementary number theoretic properties of cyclotomic polynomials are a topic that has become very popular among olympiad… (More)

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2007

2007

- Florian Breuer, Ernest Lötter, Brink van der Merwe
- Finite Fields and Their Applications
- 2007

We study Ducci-sequences using basic properties of cyclotomic polynomials over F2. We determine the period of a given Ducci… (More)

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2004

2004

- Paul Erdös
- 2004

For n<105 all coefficients of Fn(x) are ±1 or 0. For n = 10S, the coefficient 2 occurs for the first time. Denote by A w the… (More)

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2002

2002

- Kazuo Habiro
- 2002

The main object of study in this paper is the completion Z[q] = lim ←−n Z[q]/((1−q)(1−q) · · · (1−q)) of the polynomial ring Z[q… (More)

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1996

1996

- Woo Jin Oh, Yong Hoon Lee
- IEEE Signal Processing Letters
- 1996

The cyclotomic polynomial (CP) prefilter design problem is formulated as an optimization problem with linear objective functions… (More)

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1993

1993

- Richard J. Hartnett, Gloria Faye Boudreaux-Bartels
- IEEE Trans. Signal Processing
- 1993

We present an efficient FIR filter design algorithm that generalizes existing cascaded FIR prefilter-equalizer methods. We… (More)

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1992

1992

- Richard P. Brent
- ArXiv
- 1992

For odd square-free n > 1 the cyclotomic polynomial Φn(x) satisfies the identity of Gauss 4Φn(x) = An − (−1)(n−1)/2nB2 n. A… (More)

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1985

1985

- Eric Bach, Jeffrey Shallit
- 26th Annual Symposium on Foundations of Computer…
- 1985

This paper discusses some new integer factoring methods involving cyclotomic polynomials. There are several polynomials f(X… (More)

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