NON-BEITER TERNARY CYCLOTOMIC POLYNOMIALS WITH AN OPTIMALLY LARGE SET OF COEFFICIENTS
نویسندگان
چکیده
منابع مشابه
Ternary Cyclotomic Polynomials with an Optimally Large Set of Coefficients
Ternary cyclotomic polynomials are polynomials of the form Φpqr(z) = ∏ ρ(z − ρ), where p < q < r are odd primes and the product is taken over all primitive pqr-th roots of unity ρ. We show that for every p there exists an infinite family of polynomials Φpqr such that the set of coefficients of each of these polynomials coincides with the set of integers in the interval [−(p − 1)/2, (p + 1)/2]. ...
متن کاملCyclotomic polynomials with large coefficients
The coefficients a(m,n) and especially A(n) and S(n) have been the subject of numerous investigations (see [1] and the references given there). Until recently all these investigations concerned very thin sets of integers n. In [3] the author could establish a property valid for a set of integers of asymptotic density 1. Let ε(n) be any function defined for all positive integers such that limn→∞...
متن کاملCoefficients of cyclotomic polynomials
Let a(n, k) be the k-th coefficient of the n-th cyclotomic polynomial. Recently, Ji, Li and Moree [12] proved that for any integer m ≥ 1, {a(mn, k)|n, k ∈ N} = Z. In this paper, we improve this result and prove that for any integers s > t ≥ 0, {a(ns + t, k)|n, k ∈ N} = Z. 2000 Mathematics Subject Classification:11B83; 11C08
متن کاملOn Cyclotomic Polynomials with ± 1 Coefficients
We characterize all cyclotomic polynomials of even degree with coefficients restricted to the set {+1,−1}. In this context a cyclotomic polynomial is any monic polynomial with integer coefficients and all roots of modulus 1. Inter alia we characterize all cyclotomic polynomials with odd coefficients. The characterization is as follows. A polynomial P (x) with coefficients ±1 of even degree N − ...
متن کاملValues of coefficients of cyclotomic polynomials II
Let a(n, k) be the kth coefficient of the nth cyclotomic polynomial. In part I it was proved that {a(mn, k) | n ≥ 1, k ≥ 0} = Z, in case m is a prime power. In this paper we show that the result also holds true in case m is an arbitrary positive integer.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112501072