Bounds for the roots of lacunary polynomials (Q1587233)

The author obtains new upper bounds for the absolute values of the roots of a lacunary polynomial with complex coefficients. The main result is based on the study of the polynomial equation \(x^n- x^{n-1}= a\), with \(a>0\), \(n\geq 2\) and Hölder's inequality. It extends many estimates for the roots of lacunary polynomials, for example a theorem of \textit{H. Guggenheimer} [Am. Math. Mon. 69, 915-916 (1962)]. Note that the paper also contains a bound à la Cauchy. Both results are compared through examples.