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The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Restrictions On The Coefficients, Brett A. Shields Mr.

Electronic Theses and Dissertations

In this thesis, we put restrictions on the coefficients of polynomials and give bounds concerning the number of zeros in a specific region. Our results generalize a number of previously known theorems, as well as implying many new corollaries with hypotheses concerning monotonicity of the modulus, real, as well as real and imaginary parts of the coefficients separately. We worked with Enestr\"{o}m-Kakeya type hypotheses, yet we were only concerned with the number of zeros of the polynomial. We considered putting the same type of restrictions on the coefficients of three different types of polynomials: polynomials with a monotonicity``flip" at some …