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Generating functions of even Dedekind symbols with polynomial reciprocity laws

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Abstract

We will obtain generating functions of even Dedekind symbols with polynomial reciprocity laws. The generating functions are expressed in terms of Kronecker’s double series. We also establish reciprocity laws satisfied by these generating functions. As an application, we demonstrate new Eisenstein series identities which involve the derivatives of the first and second order.

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Authors and Affiliations

  1. Department of Mathematics, Tsuda College, Tsuda-machi 2-1-1, Kodaira-shi, Tokyo, 187-8577, Japan

    Shinji Fukuhara

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  1. Shinji Fukuhara
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Correspondence to Shinji Fukuhara.

Additional information

Communicated by Ulf Kühn.

The author wishes to thank Professor N. Yui for her helpful advice. This work was supported by Grant-in-Aid for Scientific Research (No. 19540101), Japan Society for the Promotion of Science.

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Fukuhara, S. Generating functions of even Dedekind symbols with polynomial reciprocity laws. Abh. Math. Semin. Univ. Hambg. 84, 139–153 (2014). https://doi.org/10.1007/s12188-014-0096-4

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  • DOI: https://doi.org/10.1007/s12188-014-0096-4

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