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
Rok vydání:	2021
Předmět:	11C08 12E05 11A41 Mathematics - Number Theory Mathematics::Number Theory General Mathematics 010102 general mathematics FOS: Mathematics Number Theory (math.NT) 010103 numerical & computational mathematics 0101 mathematics 01 natural sciences
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::66cd9083981e35f87c5345e5dae9c564 https://doi.org/10.1017/s1446788721000227 Zobrazit plný text záznamu