Computationally classifying polynomials with small Euclidean norm having reducible non-reciprocal parts
 作者： Michael Filaseta,  Robert Murphy,  Andrew Vincent 作者单位： 1Mathematics Department University of South Carolina Columbia, SC 29208, USA2Mathematics Department University of Illinois 1409 W. Green Street Urbana, IL 61801, USA3Forest 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... classification forall polynomials with norm $\le {5}^{1/2}$ and some additional sparse polynomials.

• 实行　追加的
• reciprocal　相互的
• classifying　分级
• reducible　可还原的
• author　著者
• polynomial　多项式