THE NON-CYCLOTOMIC PART OF f(x)xn + g(x) AND ROOTS OF RECIPROCAL POLYNOMIALS OFF THE UNIT CIRCLE

@inproceedings{Dobrowolski2013THENP,
  title={THE NON-CYCLOTOMIC PART OF f(x)xn + g(x) AND ROOTS OF RECIPROCAL POLYNOMIALS OFF THE UNIT CIRCLE},
  author={Edward G. Dobrowolski and Michael Filaseta and Antoine Vincent},
  year={2013}
}
Given relatively prime polynomials f(x) and g(x) in ℤ[x] with non-zero constant terms, we show that for n greater than an explicitly determined bound depending on f(x) and g(x), if the polynomial f(x)xn + g(x) is non-reciprocal, then its non-cyclotomic part is irreducible except for some explicit cases where a known factorization of f(x)xn + g(x) can easily be described. Prior work of a similar nature is discussed which shows under similar circumstances the non-reciprocal part off(x)xn + g(x… CONTINUE READING

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