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Dedekind sums for a fuchsian group, II

Published online by Cambridge University Press:  22 January 2016

Larry Joel Goldstein
Larry Joel Goldstein*
Affiliation:
University of Maryland, Department of Mathematics
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In [1] we derived a generalization of Kronecker’s first limit formula. Our generalization was a limit formula for the Eisenstein series for an arbitrary cusp of a Fuchsian group Γ of the first kind operating on the complex upper half-plane H. In that work, we introduced Dedekind sums associated to the principal congruence subgroups Γ(N) of the elliptic modular group. The work of our preceding paper suggests a natural question: Is there a generalization of Kronecker’s second limit formula to the setting of a general Fuchsian group of the first kind? The answer to this question is the subject of this paper.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 171 - 187
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Goldstein, L. Dedekind Sums for a Fuchsian Group, I, Nagoya Math. J. 50 (1973), 21–47.Google Scholar
[2] Kubota, T. Elementary Theory of Eisenstein Series, Kodansha Press, Tokyo, 1973.Google Scholar
[3] Siegel, C. L. Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1961.Google Scholar