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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Generalized Dedekind eta-functions and generalized Dedekind sums
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by Bruce C. Berndt PDF
Trans. Amer. Math. Soc. 178 (1973), 495-508 Request permission

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.
References
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 178 (1973), 495-508
  • MSC: Primary 10D05; Secondary 10H10
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0371817-5
  • MathSciNet review: 0371817