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Geometry of
trinomials
Aaron Melman |
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Vol. 259 (2012), No. 1, 141–159
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Abstract |
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The location of the zeros of a general trinomial was analyzed in the late 19th and early 20th centuries. We reexamine this problem and obtain new zero inclusion regions in the complex plane that complement and improve known results. Our main contribution is the derivation of smaller annular sectors containing the zeros of a trinomial that take into account the magnitude of the coefficients, which is unlike existing results where such sectors are rigid. |
Keywords
Rouché, trinomial, zero, root, location, bound, estimate
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Mathematical Subject Classification 2010
Primary: 12D10, 15A18, 30C15
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Milestones
Received: 5 September 2011
Revised: 17 April 2012
Accepted: 15 May 2012
Published: 31 August 2012
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Authors |
| Aaron Melman | |
| Department of Applied Mathematics,
School of Engineering Santa Clara University Santa Clara, CA 95053 United States |
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