Generalized Dedekind symbols associated with the Eisenstein series
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- by Shinji Fukuhara PDF
- Proc. Amer. Math. Soc. 127 (1999), 2561-2568 Request permission
Abstract:
We have shown recently that the space of modular forms, the space of generalized Dedekind sums, and the space of period polynomials are all isomorphic. In this paper, we will prove, under these isomorphisms, that the Eisenstein series correspond to the Apostol generalized Dedekind sums, and that the period polynomials are expressed in terms of Bernoulli numbers. This gives us a new more natural proof of the reciprocity law for the Apostol generalized Dedekind sums. Our proof yields as a by-product new polylogarithm identities.References
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Additional Information
- Shinji Fukuhara
- Affiliation: Department of Mathematics, Tsuda College, Tsuda-machi 2-1-1, Kodaira-shi, Tokyo 187, Japan
- Email: fukuhara@tsuda.ac.jp
- Received by editor(s): October 7, 1997
- Published electronically: May 4, 1999
- Additional Notes: The author wishes to thank Professor N. Yui for her useful advice
- Communicated by: Dennis A. Hejhal
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2561-2568
- MSC (1991): Primary 11F20, 11F67; Secondary 11F11, 11M35, 33E20
- DOI: https://doi.org/10.1090/S0002-9939-99-05291-0
- MathSciNet review: 1657743