The S-relative Pólya groups and S-Ostrowski quotients of number fields

2023/12/14 by Ehsan Shahoseini, Shahoseini, Ehsan, Abbas Maarefparvar +1
Computer Science · Mathematics · #11R34 #11R37 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.09362

openalex publication_date 2023/12/14 · openalex created_date 2023/12/19 · openalex updated_date 2026/07/28

Abstract

Let K/F be a finite extension of number fields and S be a finite set of primes of F, including all the archimedean ones. In this paper, using some results of González-Avilés \citeAviles, we generalize the notions of the relative Pólya group \Po(K/F) \citeChabertI,MR2 and the Ostrowski quotient \Ost(K/F) \citeSRM to their S-versions. Using this approach, we obtain generalizations of some well-known results on the S-capitulation map, including an S-version of Hilbert's theorem 94.

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