View : 58 Download: 0

Maximum gap in cyclotomic polynomials

Title
Maximum gap in cyclotomic polynomials
Authors
Al-Kateeb, Ala'aAmbrosino, MaryHong, HoonLee, Eunjeong
Ewha Authors
이은정
Issue Date
2021
Journal Title
JOURNAL OF NUMBER THEORY
ISSN
0022-314XJCR Link

1096-1658JCR Link
Citation
JOURNAL OF NUMBER THEORY vol. 229, pp. 1 - 15
Keywords
Cyclotomic polynomialsInverse cyclotomic polynomialsMaximum gap
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCIE; SCOPUS WOS 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 (Phi(p1p2) ) = p1-1 for primes p(2) > p(1). In 2017, based on numerous calculations, the following generalization was conjectured: g (Phi mp) = phi(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 Phi mp, which are divisible by the m-th inverse cyclotomic polynomial Psi(m) = xm-1. (c) 2021 Elsevier Inc. All rights reserved.
DOI
10.1016/j.jnt.2021.04.013
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE