On a class number formula for real quadratic number fields

TL;DR

This paper derives a new class number formula for real quadratic fields using Dirichlet L-series and a rapidly convergent series, providing a novel computational approach.

Contribution

It introduces a formula connecting class numbers of real quadratic fields with Dirichlet L-series evaluated at specific points and a new rapidly convergent series.

Findings

Derived a formula for L(1,psi) involving sums of L-series at s=2 and s=3

Established a class number formula for real quadratic fields

Presented a computationally efficient series for numerical evaluation

Abstract

For an even Dirichlet character psi, we obtain a formula for L(1,psi) in terms of a sum of Dirichlet L-series evaluated at s=2 and s=3 and a rapidly convergent numerical series involving the central binomial coefficients. We then derive a class number formula for real quadratic number fields by taking L(s,psi) to be the quadratic L-series associated with these fields.