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arXiv · 2012.03102

An effective analytic formula for the number of distinct irreducible factors of a polynomial

Stephan Ramon Garcia·Ethan Simpson Lee·Josh Suh·Jiahui Yu
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Abstract

We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors of a polynomial $f \in \mathbb{Z}[x]$. We use an explicit version of Mertens' theorem for number fields to estimate a related sum over rational primes. For a given $f \in \mathbb{Z}[x]$, our result yields a finite list of primes that certifies the number of distinct irreducible factors of $f$.

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Stephan Ramon Garcia, Ethan Simpson Lee, Josh Suh, Jiahui Yu. 2020-12-05. An effective analytic formula for the number of distinct irreducible factors of a polynomial. https://arxiv.org/abs/2012.03102

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