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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Generalized Dedekind eta-functions and generalized Dedekind sums

Author: Bruce C. Berndt
Journal: Trans. Amer. Math. Soc. 178 (1973), 495-508
MSC: Primary 10D05; Secondary 10H10
MathSciNet review: 0371817
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Abstract: A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.

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Keywords: Eisenstein series, Dedekind eta-function, generalized Dedekind eta-function, Dedekind sum, generalized Dedekind sum, Bernoulli numbers and polynomials, reciprocity law, Lambert series, modular transformation
Article copyright: © Copyright 1973 American Mathematical Society