Flat cyclotomic polynomials of order three

✍ Scribed by Nathan Kaplan

• Book ID: 104024866
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 126 KB
• Volume: 127
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2007.01.008

✦ Synopsis

We say that a cyclotomic polynomial Φ n has order three if n is the product of three distinct primes, p < q < r. Let A(n) be the largest absolute value of a coefficient of Φ n . For each pair of primes p < q, we give an infinite family of r such that A(pqr) = 1. We also prove that A(pqr) = A(pqs) whenever s > q is a prime congruent to ±r (mod pq).