The flatness of ternary cyclotomic polynomials

  • Bin Zhang

    Qufu Normal University, China
The flatness of ternary cyclotomic polynomials cover
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Abstract

It is well known that all of the prime cyclotomic polynomials and binary cyclotomic polynomials are flat, and the flatness of ternary cyclotomic polynomials is much more complicated. Let p<q<rp < q < r be odd primes such that zr±zr\equiv\pm (mod pqpq), where zz is a positive integer. So far, the classification of flat ternary cyclotomic polynomials for 1z51\leq z\leq 5 has been given. In this paper, for z=6z=6 and q±1q\equiv \pm 1 (mod pp), we give the necessary and sufficient conditions for ternary cyclotomic polynomials Φpqr(x)\Phi_{pqr}(x) to be flat.

Cite this article

Bin Zhang, The flatness of ternary cyclotomic polynomials. Rend. Sem. Mat. Univ. Padova 145 (2021), pp. 1–42

DOI 10.4171/RSMUP/47