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Dedekind zeta-functions and Dedekind sums

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Abstract

In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) = 1/45(26n3 -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n2 + 1, and the class number of quadratic number field K2 = Q(vq) is 1.

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Authors and Affiliations

  1. Institute of Mathematics, Tongji University, 200092, Shanghai, China

    Hongwen Lu, Rongzheng Jiao & Chungang Ji

Authors
  1. Hongwen Lu
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  2. Rongzheng Jiao
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  3. Chungang Ji
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Correspondence to Hongwen Lu.

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Lu, H., Jiao, R. & Ji, C. Dedekind zeta-functions and Dedekind sums. Sci. China Ser. A-Math. 45, 1059–1065 (2002). https://doi.org/10.1007/BF02879989

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  • DOI: https://doi.org/10.1007/BF02879989

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