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arXiv · 2109.12867

Bhargava factorials and irreducibility of integer-valued polynomials

Devendra Prasad
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Abstract

The ring of integer-valued polynomials over a given subset $S$ of $\Z$ (or $ \mathrm{Int}(S,\Z ))$ is defined as the set of polynomials in $\Q[x]$ which maps $S$ to $\Z$. In factorization theory, it is crucial to check the irreducibility of a polynomial. In this article, we make Bhargava factorials our main tool to check the irreducibility of a given polynomial $f \in \mathrm{Int}(S,\Z ))$. We also generalize our results to arbitrary subsets of a Dedekind domain.

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Devendra Prasad. 2021-09-27. Bhargava factorials and irreducibility of integer-valued polynomials. https://arxiv.org/abs/2109.12867

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