We impose a monotonicity condition with several reversals on the moduli of the coefficients of a polynomial. We then consider three types of polynomials: (1) those satisfying the condition on all of the coefficients, (2) those satisfying the condition on the even indexed and odd indexed coefficients separately, and (3) polynomials of the form P(z) = a0+ Σnj=µ ajzj where µ ≥ 1 with the coefficients aµ; aµ+1;…; an satisfying the condition. For each type of polynomial, we give a result which puts a bound on the number of zeros in a disk (in the complex plane) centered at the origin. For each type, we give an example showing the results are best possible.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16596 |
| Date | 01 January 2016 |
| Creators | Bryant, Derek, Gardner, Robert |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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