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Maximum gap in (inverse) cyclotomic polynomial

Title
Maximum gap in (inverse) cyclotomic polynomial
Authors
Hong H.Lee E.Lee H.-S.Park C.-M.
Ewha Authors
이향숙이은정
SCOPUS Author ID
이향숙scopus
Issue Date
2012
Journal Title
Journal of Number Theory
ISSN
0022-314XJCR Link
Citation
vol. 132, no. 10, pp. 2297 - 2315
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Let g(f) denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial f. Let Φ n denote the n-th cyclotomic polynomial and let Ψ n denote the n-th inverse cyclotomic polynomial. In this note, we study g(Φ n) and g(Ψ n) where n is a product of odd primes, say p 1<p 2<p 3, etc. It is trivial to determine g(Φp1), g(Ψp1) and g(Ψp1p2). Hence the simplest non-trivial cases are g(Φ p1p2) and g(Ψ p1p2p3). We provide an exact expression for g(Φ p1p2). We also provide an exact expression for g(Ψ p1p2p3) under a mild condition. The condition is almost always satisfied (only finite exceptions for each p 1). We also provide a lower bound and an upper bound for g(Ψ p1p2p3). © 2012 Elsevier Inc.
DOI
10.1016/j.jnt.2012.04.008
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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