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 Generalized self-inversive bicomplex polynomials with respect to the $j$-conjugation Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 885-895 https://doi.org/10.4134/BKMS.b200601Published online February 22, 2021Printed July 31, 2021 Yutaka Matsui, Yuhei Sato Kindai University; Kindai University Abstract : 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. Keywords : Bicomplex analysis, self-inversive polynomial MSC numbers : Primary 30G35, 13B25 Downloads: Full-text PDF   Full-text HTML