On the number of integer polynomials with multiplicatively dependent roots |
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| Authors: | A Dubickas M Sha |
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| Institution: | 1.Institute of Mathematics, Faculty of Mathematics and Informatics,Vilnius University,Vilnius,Lithuania;2.Department of Computing,Macquarie University,Sydney,Australia |
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| Abstract: | We give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include sharp lower bounds, upper bounds and asymptotic formulas for various cases, although in general there is a logarithmic gap between lower and upper bounds. |
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