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Yes, there is a generalization. It was done by Larry Joel Goldstein, in the paper "Dedekind sums for a Fuchsian group". The paper has two parts and was published in the Nagoya Journal in around 1973-74.

You can also have a look in Goldstein's book on analytic number theory, for background.

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Yes, there is a generalization. It was done by Larry Joel Goldstein, in the paper "Dedekind sums for a Fuchsian group". The paper has two parts and was published in the Nagoya Journal in around 1973-74.

You can also have a look in Goldstein's book on analytic number theory, for background.