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Resonance

, Volume 24, Issue 2, pp 239–244 | Cite as

Fundamental Theorem of Algebra – A Nevanlinna Theoretic Proof

  • Bikash ChakrabortyEmail author
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Abstract

There are several proofs of the fundamental theorem of algebra, mainly using algebra, analysis and topology. The aim of this article is to discuss the fundamental theorem of algebra as an application of Nevanlinna’s second fundamental theorem.

Keywords

Fundamental theorem of algebra Nevanlinna theory principle of mathematical induction 

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Suggested Reading

  1. [1]
    F Benjamin and R Gerhard, The Fundamental Theorem of Algebra, Springer-Verlag, New York, 1997.Google Scholar
  2. [2]
    C Fefferman, An Easy Proof of the Fundamental Theorem of Algebra, Amer. Math. Monthly, Vol.74, pp.854–855, 1967.CrossRefGoogle Scholar
  3. [3]
    R P Boas, Jr., A Proof of the Fundamental Theorem of Algebra, Amer. Math. Monthly, Vol.42, No.8, pp.501–502, 1935.CrossRefGoogle Scholar
  4. [4]
    R P Boas, Jr., Yet Another Proof of the Fundamental Theorem of Algebra, Amer. Math. Monthly, Vol.71, No.2, p.180, 1964.CrossRefGoogle Scholar
  5. [5]
    B Chakraborty, A Simple Proof of the Fundamental Theorem of Algebra, The Mathematics Student, Vol.85, Nos.3–4, pp.103–104, 2016.Google Scholar
  6. [6]
    R L Thompson, Open Mappings and the Fundamental Theorem of Algebra, Math. Mag., Vol.43, No.1, pp.39–40, 1970.CrossRefGoogle Scholar
  7. [7]
    A Abian, A New Proof of the Fundamental Theorem of Algebra, Caribbean J. Math., Vol.5, No.1, pp.9–12, 1986.Google Scholar
  8. [8]
    D J Velleman, Another Proof of the Fundamental Theorem of Algebra, Math. Mag., Vol.70, pp.216–217, 1997.CrossRefGoogle Scholar
  9. [9]
    R Nevanlinna, Zur Theorie der meromorphen Funktionen, Acta Math., Vol.46, No.1–2, pp.1–99, 1925.CrossRefGoogle Scholar
  10. [10]
    W K Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.Google Scholar
  11. [11]
    W Dunham, Euler and the Fundamental Theorem of Algebra, College Math. J., Vol.22, pp.282–293, 1991.CrossRefGoogle Scholar
  12. [12]
    M D Hirschhorn, The Fundamental Theorem of Algebra, College Math. J., Vol.29, pp.276–277, 1998.CrossRefGoogle Scholar
  13. [13]
    R Redheffer, The Fundamental Theorem of Algebra, Amer. Math. Monthly, Vol.64, pp.582–585, 1957.Google Scholar
  14. [14]
    F Terkelsen, The Fundamental Theorem of Algebra, Amer. Math. Monthly, Vol.83, p.647, 1976.CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Ramakrishna MissionVivekananda Centenary CollegeRaharaIndia

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