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수리과학연구소
Journal papers
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Maximum gap in cyclotomic polynomials
Title
Maximum gap in cyclotomic polynomials
Authors
Al-Kateeb A.
;
Ambrosino M.
;
Hong H.
;
Lee E.
Ewha Authors
이은정
SCOPUS Author ID
이은정
Issue Date
2021
Journal Title
Journal of Number Theory
ISSN
0022-314X
Citation
Journal of Number Theory vol. 229, pp. 1 - 15
Keywords
Cyclotomic polynomials
;
Inverse cyclotomic polynomials
;
Maximum gap
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We study the maximum gap g (maximum of the differences between any two consecutive exponents) of cyclotomic polynomials. In 2012, Hong, Lee, Lee and Park showed that g(Φp1p2)=p1−1 for primes p2>p1. In 2017, based on numerous calculations, the following generalization was conjectured: g(Φmp)=φ(m) for square free odd m and prime p>m. The main contribution of this paper is a proof of this conjecture. The proof is based on the discovery of an elegant structure among certain sub-polynomials of Φmp, which are divisible by the m-th inverse cyclotomic polynomial Ψm=[Formula presented]. © 2021 Elsevier Inc.
DOI
10.1016/j.jnt.2021.04.013
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