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- W1481896174 abstract "We build a new theory for analyzing the coefficients of any cyclotomic polynomial by considering it as a gcd of simpler polynomials. Using this theory, we generalize a result known as periodicity and provide two new families of flat cyclotomic polynomials. One, of order 3, was conjectured by Broadhurst: $Phi_{pqr}(x)$ is flat where $p<q<r$ are primes and there is a positive integer $w$ such that $requivpm wpmod{pq}$, $pequiv1pmod w$ and $qequiv1pmod{wp}$. The other is the first general family of order 4: $Phi_{pqrs}(x)$ is flat for primes $p,q,r,s$ where $qequiv-1pmod p$, $requivpm1pmod{pq}$, and $sequivpm1pmod{pqr}$. Finally, we prove that the natural extension of this second family to order 5 is never flat, suggesting that there are no flat cyclotomic polynomials of order 5." @default.
- W1481896174 created "2016-06-24" @default.
- W1481896174 creator A5047346803 @default.
- W1481896174 date "2012-07-24" @default.
- W1481896174 modified "2023-09-27" @default.
- W1481896174 title "Flat Cyclotomic Polynomials: A New Approach" @default.
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