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Explicit formulas for Hecke Gauss sums in quadratic number fields

  • Hatice Boylan
  • Nils-Peter Skoruppa
Article

Abstract

We derive an explicit formula for Hecke Gauss sums of quadratic number fields. As an immediate consequence we obtain a quadratic reciprocity law in quadratic number fields which generalizes the classical one given by Hecke. The proofs use, apart from the well-known formulas for ordinary Gauss sums, only elementary algebraic manipulations.

Keywords

Hecke reciprocity Gauss sums 

Mathematics Subject Classification (2000)

11L05 

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Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2010

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität SiegenSiegenGermany
  2. 2.Matematik BölümüBilkent ÜniversitesiAnkaraTurkey

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