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Zur Lage der kritischen Punkte eines Polynoms. (The position of critical points of a polynomial). (German) Zbl 0231.30001


MSC:

30C10 Polynomials and rational functions of one complex variable
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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References:

[1] Biernacki , M. : Sur les zéros des polynomes , Ann. Mariae Curie-Skłodowska Sect. A . 9 , 81 - 98 ( 1957 ). Zbl 0079.02301 · Zbl 0079.02301
[2] Brannan , D.A. : On a conjecture of Ilieff , Proc. Camb. Phil. Soc. 64 , 83 - 85 ( 1968 ). MR 220906 | Zbl 0163.30901 · Zbl 0163.30901
[3] Ganelius , T. : Sequences of analytic functions and their zeros , Arkiv för Mat. 3 , 1 - 50 ( 1953 ). MR 62826 | Zbl 0055.06905 · Zbl 0055.06905 · doi:10.1007/BF02589280
[4] Goodman , A.W. , Rahman , Q.I. and Ratti , J.S. : On the zeros of a polynomial and its derivative , Proc. Amer. Math. Soc. 21 , 273 - 274 ( 1969 ). MR 239062 | Zbl 0172.35903 · Zbl 0172.35903 · doi:10.2307/2036982
[5] Joyal , A. : On the zeros of a polynomial and its derivative , J. Math. Anal. Appl. 26 , 315 - 317 ( 1969 ). MR 239061 | Zbl 0204.38902 · Zbl 0204.38902 · doi:10.1016/0022-247X(69)90155-3
[6] Marden , M. : The geometry of the zeros of a polynomial in a complex variable , Math. Surveys , Vol. 3 , New York : Amer. Math. Soc. 1949 . MR 31114 | Zbl 0038.15303 · Zbl 0038.15303
[7] Meir , A. and Sharma , A. : On Ilyeff’s conjecture , Pacific J. Math. 31 , 459 - 467 ( 1969 ). Article | MR 249587 | Zbl 0194.10202 · Zbl 0194.10202 · doi:10.2140/pjm.1969.31.459
[8] Rubinstein , Z. : On a problem of Ilyeff , Pacific J. Math. 26 , 159 - 161 ( 1969 ). Article | MR 237753 | Zbl 0172.35902 · Zbl 0172.35902 · doi:10.2140/pjm.1968.26.159
[9] Saff , E.B. and Twomey , J.B. : A note on the location of critical points of polynomials , Proc. Amer. Math. Soc. 27 , 303 - 308 ( 1971 ). MR 271312 | Zbl 0218.30002 · Zbl 0218.30002 · doi:10.2307/2036310
[10] Schmeisser , G. : Bemerkungen zu einer Vermutung von Ilieff , Math. Z. 111 , 121 - 125 ( 1969 ). Article | MR 264040 | Zbl 0176.36703 · Zbl 0176.36703 · doi:10.1007/BF01111192
[11] Specht , W. : Algebraische Gleichungen mit reellen oder komplexen Koeffizienten, Enzyklop. d. math. Wissensch. I, 1 , Heft 3 , II, Stuttgart : Teubner 1958 . MR 106274 | Zbl 0082.24503 · Zbl 0082.24503
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