The number of zeros of a polynomial in a disk as a consequence of restrictions on the coefficients

  • Robert Gardner Department of Mathematics and Statistics, East Tennessee State University, Johnson City, Tennessee 37614-0663
  • Brett Shields Department of Mathematics and Statistics, East Tennessee State University, Johnson City, Tennessee 37614-0663
Keywords: polynomials, counting zeros, monotone coefficients

Abstract

We put restrictions on the coefficients of polynomials and give bounds concerning the number of zeros in a specific region. The restrictions involve a monotonicity-type condition on the coefficients of the even powers of the variable and on the coefficients of the odd powers of the variable (treated separately). We present results by imposing the restrictions on the moduli of the coefficients, the real and imaginary parts of the coefficients, and the real parts (only) of the coefficients.

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Published
2015-12-31
Section
Articles