Abstract

The absolute separation of a polynomial is the minimum nonzero difference between the absolute values of its roots. In the case of polynomials with integer coefficients, it can be bounded from below in terms of the degree and the height (the maximum absolute value of the coefficients) of the polynomial. We improve the known bounds for this problem and related ones. Then we report on extensive experiments in low degrees, suggesting that the current bounds are still very pessimistic.

中文翻译：

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绝对根分离

摘要

多项式的绝对间隔是其根的绝对值之间的最小非零差。在具有整数系数的多项式的情况下，它可以根据多项式的次数和高度（系数的最大绝对值）从下方限定。我们改进了这个问题和相关问题的已知界限。然后我们报告了低程度的广泛实验，表明当前的界限仍然非常悲观。