AN EFFECTIVE ANALYTIC FORMULA FOR THE NUMBER OF DISTINCT IRREDUCIBLE FACTORS OF A POLYNOMIAL
Autor: | STEPHAN RAMON GARCIA, ETHAN SIMPSON LEE, JOSH SUH, JIAHUI YU |
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Rok vydání: | 2021 |
Předmět: | |
Zdroj: | Journal of the Australian Mathematical Society. 113:339-356 |
ISSN: | 1446-8107 1446-7887 |
Popis: | 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 $f$. Comment: 15 pages |
Databáze: | OpenAIRE |
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