Korean Journal of Mathematics

  • 제30권2호
  • /
  • Pages.187-198
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  • 2022
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ON ζ-FACTORS AND COMPUTING STRUCTURES IN CYCLIC n-ROOTS

  • Sabeti, Rostam (Great Lakes Association for Algebra and Computation (GLAAC), A Formation for Elite college students in the State of Michigan)
  • 투고 : 2021.06.01
  • 심사 : 2022.05.03
  • 발행 : 2022.06.30
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초록

In this paper, we introduce a new concept in number theory called ζ-factors associated with a positive integer n. Applications of ζ-factors are in the arrangement of the defining polynomials in cyclic n-roots algebraic system and are thoroughly investigated. More precisely, ζ-factors arise in the proofs of vanishing theorems in regard to associated prime factors of the system. Exact computations through concrete examples of positive dimensions for n = 16, 18 support the results.

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과제정보

I am grateful to the anonymous referees for their invaluable comments.

참고문헌

  1. W.W. Adams and P. Loustanau, An Introduction to Grobner Bases, Graduate Studies in Mathematics, American Mathematical Society, 1996.
  2. I. Niven, H. S. Zuckerman and H. L. Montgomery, An introduction to the theory of numbers, John Wiley & Sons. Inc. New York, Chichester, Brisbane, Toronto, Singapore, 1991.
  3. R. Sabeti, Scheme of cyclic 9-roots. A heuristic numerical-symbolic approach, Bull. Math. Soc. Sci. Math. Roum. Tome 58 (106) (2015), 199-209.
  4. R. Sabeti, Polynomial expressions for non-binomial structures, Theo. Compu. Sci. Vol. 762 (2019), 13-24. https://doi.org/10.1016/j.tcs.2018.10.020