The class number formula for imaginary quadratic fields

2015/02/17 by Joseph Lewittes, Lewittes, Joseph
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1502.04971

openalex publication_date 2015/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the class number for negative discriminant D can be expressed in terms of the base B expansions of reduced fractions (x)/(|D|), where B is an integer prime to D. This result is then formulated to obtain information about the distribution of the values of χ(x), where χ is the quadratic character associated to D. This leads to simplified formulas for the class number in certain cases.

Related

• The number of imaginary quadratic fields with a given class number
• Class Number Formulas for Certain Biquadratic Fields
• The number of imaginary quadratic fields with prime discriminant and\n class number up to H
• Algebraic functions and class number formulas
• Class number of real quadratic fields of explicit discriminant