Some congruences on prime factors of class number of algebraic extensions K/Q

2002/12/20 by Roland Quême, Roland Queme, Queme, Roland
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0212419

arxiv created 2002/12/20 · openalex publication_date 2002/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is an updated version of ANT-0372 (2002 dec 4) with the same title. Several errors are corrected in this version. An example of the kind of results obtained is: Let K/\Q be an abelian extension with N = [K:\Q] > 1, N odd. Let h(K) be the class number of K. Suppose that h(K) > 1. Let p be a prime dividing h(K). Let r_p be the rank of the p-class group of K. Then p × (p^r_p-1) and N are not coprime. The paper is at elementary level and contains a lot of numerical examples.

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