On the average of the number of imaginary quadratic fields with a given class number

2015/12/22 by Lamzouri, Youness
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1512.07134

Abstract

Let F(h) be the number of imaginary quadratic fields with class number h. In this note, we improve the error term in Soundararajan's asymptotic formula for the average of F(h). Our argument leads to a similar refinement of the asymptotic for the average of F(h) over odd h, which was recently obtained by Holmin, Jones, Kurlberg, McLeman and Petersen.

Related

• The number of imaginary quadratic fields with a given class number
• The number of imaginary quadratic fields with prime discriminant and\n class number up to H
• Missing class groups and class number statistics for imaginary quadratic fields
• Averages and moments associated to class numbers of imaginary quadratic fields
• Counting extensions of imaginary quadratic fields