On a class number formula for real quadratic number fields

For an even Dirichlet character ψ, we obtain a formula for L (1, ψ) 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 ta...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2002-04, Vol.65 (2), p.259-270
Main Authors: Bradley, David M., Özlük, Ali E., Snyder, C.
Format: Article
Language:English
Subjects:
Binomial coefficients
Dirichlet problem
Number theory
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Summary:For an even Dirichlet character ψ, we obtain a formula for L (1, ψ) 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, ψ) to be the quadratic L-series associated with these fields.
ISSN:0004-9727
1755-1633
DOI:10.1017/S000497270002030X