Dedekind sums and class numbers of imaginary abelian number fields

2023/03/24 by Stéphane Louboutin, Louboutin, Stéphane
Mathematics · #11F20 #11M20 #11R11 #11R20 #11R29 #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.14000

openalex publication_date 2023/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As a consequence of their work, Bruce C. Berndt and Ronald J. Evans in 1977 and Larry Joel Goldstein and Michael Razar in 1976 obtained a formula for the square of the class number of an imaginary quadratic number field in terms of Dedekind sums. Here we focus only on this formula and give a new short and simple proof of it. We finally express the relative class numbers of imaginary abelian number fields in terms of Dedekind sums.

Related

• The class number formula for imaginary quadratic fields
• Sums of the floor function related to class numbers of imaginary quadratic fields
• Notes on the divisibility of the class numbers of certain imaginary quadratic fields
• Algebraic functions and class number formulas
• The number of imaginary quadratic fields with a given class number