[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170684

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)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1305-1320 More about this Journal

Abstract

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.

Keywords

fixed divisor; generalized factorial; Dedekind domain;

Citations & Related Records

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