Computationally classifying polynomials with small Euclidean norm having reducible non-reciprocal parts
作者: Michael FilasetaRobert MurphyAndrew Vincent
作者单位: 1Mathematics Department University of South Carolina Columbia, SC 29208, USA
2Mathematics Department University of Illinois 1409 W. Green Street Urbana, IL 61801, USA
3Forest City Gear 11715 Main Street Roscoe, IL 61073, USA
刊名: Banach Center Publications, 2019, Vol.118 , pp.245-259
来源数据库: Institute of Mathematics Polish Academy of Sciences
DOI: 10.4064/bc118-15
原始语种摘要: Let $f(x)$ be a polynomial with integer coefficients.If either $f(x) = x^{{\rm deg}\,{f}}f(1/x)$ or $f(x) = -x^{{\rm deg}\,{f}}f(1/x)$, then $f(x)$ is called reciprocal.We refer to the non-reciprocal part of $f(x)$ as the polynomial $f(x)$ removedof each of its irreducible reciprocal factors in ${\mathbb Z}[x]$ with a positive leading coefficient.In $1970$, Schinzel proved that for a given collection of $r + 1$ integers$a_0,\dots ,a_r$it is possible to classify the positive integers $d_1,\dots ,d_r$for which the non-reciprocal part of $a_0 + a_1x^{d_1} + .\kern1.3pt.\kern1.3pt. + a_rx^{d_r}$ is reducible.Specific classification results have been given bySelmer, Tverberg, Ljunggren, Mills, Schinzel, Solan, and the first author.We extend an approach of the first author to complete a similar...
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  • 实行 追加的
  • reciprocal 相互的
  • classifying 分级
  • reducible 可还原的
  • author 著者
  • polynomial 多项式
  • additional 追加的
  • complete 追加的
  • called 被呼叫的
  • sparse 稀疏的
  • either 任何