Skoči na glavni sadržaj

Glasnik matematički, Vol. 56 No. 2, 2021.

Izvorni znanstveni članak

https://doi.org/10.3336/gm.56.2.03

A remark on flat ternary cyclotomic polynomials

Bin Zhang ; School of Mathematical Sciences, Qufu Normal University, 273165 Qufu, P. R. China

Puni tekst: engleski pdf 225 Kb

str. 241-261

preuzimanja: 116

citiraj

Preuzmi JATS datoteku

Sažetak

Let \(\Phi_n(x)\) be the \(n\)-th cyclotomic
polynomial. In this paper, for odd primes \(p\lt q \lt r\)
with \(q\equiv \pm1\pmod p\) and \(8r\equiv \pm1\pmod {pq}\), we
prove that the coefficients of \(\Phi_{pqr}(x)\) do not exceed \(1\) in modulus if and only if
(i) \(p=3\), \(q\geq 19\) and \(q\equiv 1\pmod 3\) or
(ii) \(p=7\), \(q\geq83\) and \(q\equiv -1\pmod 7\).

Ključne riječi

Flat cyclotomic polynomial, ternary cyclotomic polynomial, coefficients of cyclotomic polynomial

Hrčak ID:

267203

URI

https://hrcak.srce.hr/267203

Datum izdavanja:

23.12.2021.

Posjeta: 312 *

Publication date: 31 December 2021

Volume: Vol 56

Issue: Svezak 2

Pages: 241-261

DOI: https://doi.org/10.3336/gm.56.2.03

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Flat cyclotomic polynomial, ternary cyclotomic polynomial, coefficients of cyclotomic polynomial

A remark on flat ternary cyclotomic polynomials

Bin Zhang[1]

Email: zhangbin100902025@163.com

 

[1] School of Mathematical Sciences, Qufu Normal University, 273165 Qufu, P. R. China

Abstract

Let \(\Phi_n(x)\) be the \(n\)-th cyclotomic polynomial. In this paper, for odd primes \(p\lt q \lt r\) with \(q\equiv \pm1\pmod p\) and \(8r\equiv \pm1\pmod {pq}\), we prove that the coefficients of \(\Phi_{pqr}(x)\) do not exceed \(1\) in modulus if and only if (i) \(p=3\), \(q\geq 19\) and \(q\equiv 1\pmod 3\) or (ii) \(p=7\), \(q\geq83\) and \(q\equiv -1\pmod 7\).

This display is generated from NISO JATS XML with jats-html.xsl. The XSLT engine is libxslt.