https://orcid.org/0000-0002-8621-5699
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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.
Declaration of Interest
No potential conflict of interest was reported by the authors.
Additional information
Funding
W. Fang and B. Salvy were supported in part by Agence Nationale de la Recherche (FastRelax ANR-14-CE25-0018-01). A. Dujella and T. Pejković were supported by the Croatian Science Foundation under the project no. IP-2018-01-1313 and the QuantiXLie Center of Excellence, a project co-financed by the Croatian Government and European Union through the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme (Grant no. KK.01.1.1.01.0004). Y. Bugeaud, A. Dujella, T. Pejković, and B. Salvy were supported in part by the French-Croatian bilateral COGITO project “Approximation diophantienne et courbes elliptiques.”