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International Workshop on the Arithmetic of Finite Fields

WAIFI 2008: Arithmetic of Finite Fields pp 11–18Cite as

Finite Dedekind Sums

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5130))

Abstract

In this paper, we introduce Dedekind sums associated to lattices defined over finite fields. We establish the reciprocity law for them.

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References

  1. Apostol, T.M.: Modular Functions and Dirichlet Series in Number Theory. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  2. Gekeler, E.-U.: Finite modular forms. Finite Fields and Their Applications 7, 553–572 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Goss, D.: The algebraist’s upper half-planes. Bull. Amer. Math. Soc. 2, 391–415 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  4. Goss, D.: Basic Structures of Function Fields. Springer, Heidelberg (1996)

    Google Scholar 

  5. Hamahata, Y.: Dedekind sums for finite fields. In: Diophantine Analysis and Related Fields: DARF 2007/2008. AIP Conference Proceedings, vol. 976, pp. 96–102 (2008)

    Google Scholar 

  6. Okada, S.: Analogies of Dedekind sums in function fields. Mem. Gifu Teach. Coll. 24, 11–16 (1989), http://ci.nii.ac.jp/naid/110004649314/

    Google Scholar 

  7. Rademacher, H., Grosswald, E.: Dedekind Sums, The Mathematical Association of America, Washington (1972)

    Google Scholar 

  8. Sczech, R.: Dedekindsummen mit elliptischen Funktionen. Invent. Math. 76, 523–551 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Serre, J.-P.: Cours d’arithmétique, Presses Universitaires de France, Paris (1970)

    Google Scholar 

  10. Zagier, D.: Higher-dimensional Dedekind sums. Math. Ann. 202, 149–172 (1973)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tokyo University of Science, Noda, Chiba, 278-8510, Japan

    Yoshinori Hamahata

Authors
  1. Yoshinori Hamahata
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Editor information

Joachim von zur Gathen José Luis Imaña Çetin Kaya Koç

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Hamahata, Y. (2008). Finite Dedekind Sums. In: von zur Gathen, J., Imaña, J.L., Koç, Ç.K. (eds) Arithmetic of Finite Fields. WAIFI 2008. Lecture Notes in Computer Science, vol 5130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69499-1_2

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  • DOI: https://doi.org/10.1007/978-3-540-69499-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69498-4

  • Online ISBN: 978-3-540-69499-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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