대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권4호
  • /
  • Pages.885-895
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  • 2021
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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GENERALIZED SELF-INVERSIVE BICOMPLEX POLYNOMIALS WITH RESPECT TO THE j-CONJUGATION

  • 투고 : 2020.07.13
  • 심사 : 2020.12.09
  • 발행 : 2021.07.31
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초록

In this paper, we study a kind of self-inversive polynomials in bicomplex algebra. For a bicomplex polynomial, this is the study of a relation between a kind of symmetry of its coefficients and a kind of symmetry of zeros. For our deep study, we define several new levels of self-inversivity. We prove some functional equations for standard ones, a decomposition theorem for generalized ones and a comparison theorem. Although we focus the j-conjugation in our study, our argument can be applied for other conjugations.

키워드

과제정보

The authors would like to express our gratitude to Professor K. Ihara and the referee for several useful comments.

참고문헌

  1. S. Ahmadi and M. Bidkham, Self-inversive bicomplex polynomials, Punjab Univ. J. Math. (Lahore) 48 (2016), no. 1, 55-64.
  2. D. Joyner and T. Shaska, Self-inversive polynomials, curves, and codes, in Higher genus curves in mathematical physics and arithmetic geometry, 189-208, Contemp. Math., 703, Amer. Math. Soc., Providence, RI, 2018. https://doi.org/10.1090/conm/703/14138
  3. J. E. Kim and K. H. Shon, Properties of regular functions with values in bicomplex numbers, Bull. Korean Math. Soc. 53 (2016), no. 2, 507-518. https://doi.org/10.4134/BKMS.2016.53.2.507
  4. M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, and A. Vajiac, Bicomplex holomorphic functions, Frontiers in Mathematics, Birkhauser/Springer, Cham, 2015. https://doi.org/10.1007/978-3-319-24868-4
  5. M. Marden, Geometry of polynomials, Second edition. Mathematical Surveys, No. 3, American Mathematical Society, Providence, RI, 1966.
  6. Y. Matsui and Y. Sato, Characterization theorems of Riley type for bicomplex holomorphic functions, Commun. Korean Math. Soc. 35 (2020), no. 3, 825-841. https://doi.org/10.4134/CKMS.c190323
  7. P. J. O'Hara and R. S. Rodriguez, Some properties of self-inversive polynomials, Proc. Amer. Math. Soc. 44 (1974), 331-335. https://doi.org/10.2307/2040432
  8. C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), no. 3, 413-467. https://doi.org/10.1007/BF01443559