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New identities involving sums of the tails related to real quadratic fields

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Abstract

In previous work, the authors discovered new examples of q-hypergeometric series related to the arithmetic of \(\mathbb {Q}(\sqrt{2})\) and \(\mathbb{Q}(\sqrt{3})\). Building on this work, we construct in this paper sum of the tails identities for which some which some of these functions occur as error terms. As an application, we obtain formulas for the generating function of a certain zeta functions for real quadratic fields at negative integers.

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Authors and Affiliations

  1. Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany

    Kathrin Bringmann & Ben Kane

Authors
  1. Kathrin Bringmann
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  2. Ben Kane
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Correspondence to Kathrin Bringmann.

Additional information

The first author was partially supported by NSF grant DMS-0757907 and the Alfried Krupp prize.

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Bringmann, K., Kane, B. New identities involving sums of the tails related to real quadratic fields. Ramanujan J 23, 243–251 (2010). https://doi.org/10.1007/s11139-009-9178-9

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  • DOI: https://doi.org/10.1007/s11139-009-9178-9

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