The first author [1] proved that all zeros of the reciprocal polynomial of degree with real coefficients (i.e. and for all ) are on the unit circle, provided that Moreover, the zeros of are near to the st roots of unity (except the root ). A. Schinzel [3] generalized the first part of Lakatos' result for self-inversive polynomials i.e. polynomials for which and for all with a fixed He proved that all zeros of are on the unit circle, provided that If the inequality is strict the zeros are single. The aim of this paper is to show that for real reciprocal polynomials of odd degree Lakatos' result remains valid even if We conjecture that Schinzel's result can also be extended similarly: all zeros of are on the unit circle if is self-inversive and
展开▼
机译：第一作者[1]证明，具有实系数的倒数多项式的所有零（即对所有）都在单位圆上，条件是，此外，的零都在单位的st根附近（根除外）。 ）。 A. Schinzel [3]推广了Lakatos结果的第一部分，即自反多项式，即对于所有条件都是固定的多项式，他证明了所有零都在单位圆上，只要不等式严格，则零是单身。本文的目的是表明，即使我们猜想Schinzel的结果也可以类似地扩展，对于奇数次的实数倒数多项式Lakatos的结果仍然有效：如果所有的零都是自逆的，则单位圆上的所有零都在单位圆上
展开▼
