In this paper we prove that Sendov's conjecture is true for polynomials of degree Ž . n s 6 we even determine the so-called extremal polynomials in this case , as well as for polynomials with at most six different zeros. We then generalize this last Ž . Ž . result to polynomials of degree n with at
✦ LIBER ✦
On Sendov′s Conjecture for Roots Near the Unit Circle
✍ Scribed by M.J. Miller
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 232 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0022-247X
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Plane elasticity problems that can be reduced to singular integral equations over the unit circle are considered, the method of using a dislocation density function 4.) is adopted. First, the trapezoidal approximation is modified for the evaluation of the contour integral $? [w(a)/(.-z)]da at the co