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ON THE ZEROS OF SELF-RECIPROCAL POLYNOMIALS SATISFYING CERTAIN COEFFICIENT CONDITIONS

이정희|김선홍
대한수학회 (The Korean Mathematical Society)|2010.11|대한수학회보 (Bulletin of the KMS)|제47권 제6호|pp. 1189-1194

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참고문헌

키워드

zerosself-reciprocal polynomialsunit circle
주제분류수학

초록

Kim and Park investigated the distribution of zeros around the unit circle of real self-reciprocal polynomials of even degrees with five terms, where the absolute value of middle coefficient equals the sum of all other coefficients. In this paper, we extend some of their results to the same kinds of polynomials with arbitrary many nonzero terms.

Abstract

Kim and Park investigated the distribution of zeros around the unit circle of real self-reciprocal polynomials of even degrees with five terms, where the absolute value of middle coefficient equals the sum of all other coefficients. In this paper, we extend some of their results to the same kinds of polynomials with arbitrary many nonzero terms.

참고문헌 (12)

  1. G. Ancochea, "Zeros of self-inversive polynomials", Proc. Amer. Math. Soc., 4, pp.900~902 (1953)
  2. F. F. Bonsall, "Zeros of self-inversive polynomials", Proc. Amer. Math. Soc., 3, pp.471~475 (1952)
  3. A. Cohn, "Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise", Math. Z., 14(1), pp.110~148 (1922)
  4. 김선홍, "The zeros of certain family of self-reciprocal polynomials", 대한수학회보, 44(3), pp.461~473 (2007), 대한수학회
  5. S.-H. Kim, "On the zeros of certain self-reciprocal polynomials", J. Math. Anal. Appl., 339(1), pp.240~247 (2008)
  6. P. Lakatos, "On zeros of reciprocal polynomials", Publ. Math. Debrecen, 61(3), pp.645~661 (2002)
  7. P. Lakatos, "Circular interlacing with reciprocal polynomials", Math. Inequal. Appl., 10(4), pp.761~769 (2007)
  8. P. Lakatos, "Self-inversive polynomials whose zeros are on the unit circle", Publ. Math. De-brecen, 65(3), pp.409~420 (2004)
  9. P. Lakatos, "On zeros of reciprocal polynomials of odd degree", J. Inequal. Pure Appl. Math., 4(3), pp.8~ (2003)
  10. L. Losonczi, "On reciprocal polynomials with zeros of modulus one", Math. Inequal. Appl., 9(2), pp.289~298 (2006)
  11. L. Losonczi, "Self-inversive polynomials of odd degree", Ramanujan J., 14(2), pp.305~320 (2007)
  12. A. Schinzel, "Self-inversive polynomials with all zeros on the unit circle", Ramanujan J., 9(1), pp.19~23 (2005)

관련 논문AI추천

ON ZERO DISTRIBUTIONS OF SOME SELF-RECIPROCAL POLYNOMIALS WITH REAL COEFFICIENTS김선홍, 박정훈, 한승우한국수학교육학회 · 이론수학과 교직수학2017 · 제24권 제2호ON SOME COMBINATIONS OF SELF-RECIPROCAL POLYNOMIALS김선홍대한수학회 · 대한수학회논문집2012 · 제27권 제1호Self-reciprocal polynomials with related maximal zeros김선홍, 배재국대한수학회 · 대한수학회보2013 · 제50권 제3호On self-reciprocal polynomials at a point on the unit circle김선홍대한수학회 · 대한수학회보2009 · 제46권 제6호On Zeros of Polynomials with Restricted CoefficientsAb Liman, Irshad Ahmad, Tawheeda Rasool경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제4호On the zeros of generalized derivative of a polynomialIrfan Ahmad Wani, Ishfaq Nazir, Mohammad Ibrahim Mir강원경기수학회 · 한국수학논문집2023 · 제31권 제1호

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