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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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The location of the zeros of polynomials with complex coefficients
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by Evelyn Frank PDF
Bull. Amer. Math. Soc. 52 (1946), 890-898
References
    1. R. L. Dietzold, The isograph–a mechanical root-finder, Bell Laboratories Record vol. 16 (1937) pp. 130-134.
  • Evelyn Frank, On the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc. 52 (1946), 144–157. MR 14509, DOI 10.1090/S0002-9904-1946-08526-2
  • Thornton C. Fry, Some numerical methods for locating roots of polynomials, Quart. Appl. Math. 3 (1945), 89–105. MR 12910, DOI 10.1090/S0033-569X-1945-12910-1
    • 4. J. Grommer, Ganze transzendente Funktionen mit lauter reellen Nullstellen, J. Reine Angew. Math. vol. 144 (1914) pp. 114-165.
  • Frank L. Hitchcock, Algebraic equations with complex coefficients, J. Math. Phys. Mass. Inst. Tech. 18 (1939), 202–210. MR 183, DOI 10.1002/sapm1939181202
  • A. Hurwitz, Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt, Math. Ann. 46 (1895), no. 2, 273–284 (German). MR 1510884, DOI 10.1007/BF01446812
    • 7. A. Hurwitz, Über die Nullstellen der Bessel’schen Funktion, Math. Ann. vol. 33 (1889) pp. 246-266 (Werke, vol. 1, pp. 266-286). 8. A. Hurwitz, Über einen Satz des Herrn. Kakeya, Tôhoku Math. J. vol. 4 (1913) pp. 89-93 (Werke, vol. 2, pp. 627-631). 9. A. J. Kempner, On the complex roots of algebraic equations, Bull. Amer. Math. Soc. vol. 41 (1935) pp. 809-843. 10. J. L. Lagrange, Traité de la résolution des équations numériques de tous les Degrés, Oeuvres, vol. 5, Coucier, Paris, 1808. 11. O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Leipzig, 1929. 12. C. Runge, Separation und Approximation der Wurzeln, Encyklopädie der Mathematischen Wissenschaften I, 1, Teubner, Leipzig, 1898, pp. 404-448. 13. C. Runge, Praxis der Gleichungen, Sammlung Schubert, no. 14, Göschen, Leipzig, 1900. 14. C. Runge and H. König, Vorlesungen über numerisches Rechnen, Die Grundlehren der Mathematischen Wissenschaften, vol. 11, Springer, Berlin, 1924. 15. I. Schur, Über Potenzreihen, die im lnnern des Einheitskreises beschränkt sind, J. Reine Angew. Math. vol. 147 (1917) pp. 205-232; vol. 148 (1918) pp. 122-145.
  • E. B. Van Vleck, A sufficient condition for the maximum number of imaginary roots of an equation of the $n$-th degree, Ann. of Math. (2) 4 (1903), no. 4, 191–192. MR 1502310, DOI 10.2307/1967334
Additional Information
  • Journal: Bull. Amer. Math. Soc. 52 (1946), 890-898
  • DOI: https://doi.org/10.1090/S0002-9904-1946-08668-1
  • MathSciNet review: 0017440