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Journal of the Korean Mathematical Society = 대한수학회지 v.55 no.6, 2018년, pp.1305 - 1320   SCIE
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FIXED DIVISOR OF A MULTIVARIATE POLYNOMIAL AND GENERALIZED FACTORIALS IN SEVERAL VARIABLES

Rajkumar, Krishnan   (School of Computer & Systems Sciences Jawaharlal Nehru University  ); Reddy, Arikatla Satyanarayana   (Department of Mathematics Shiv Nadar University  ); Semwal, Devendra Prasad   (Department of Mathematics Shiv Nadar University  );
  • 초록

    We define new generalized factorials in several variables over an arbitrary subset ${\underline{S}}{\subseteq}R^n$ , where R is a Dedekind domain and n is a positive integer. We then study the properties of the fixed divisor $d(\underline{S},f)$ of a multivariate polynomial $f{\in}R[x_1,x_2,{\ldots},x_n ] $ . We generalize the results of Polya, Bhargava, Gunji & McQuillan and strengthen that of Evrard, all of which relate the fixed divisor to generalized factorials of ${\underline{S}}$ . We also express $d(\underline{S},f)$ in terms of the images $f({\underline{a}})$ of finitely many elements ${\underline{a}}{\in}R^n$ , generalizing a result of Hensel, and in terms of the coefficients of f under explicit bases.


  • 주제어

    fixed divisor .   generalized factorial .   Dedekind domain.  

  • 참고문헌 (18)

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    18. P.-J. Cahen, Polynomes a valeurs entieres, Canad. J. Math. 24 (1972), 747-754. 

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