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Explicit formulas for Hecke Gauss sums in quadratic number fields

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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.

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Correspondence to Nils-Peter Skoruppa.

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Communicated by U. Kühn.

During the preparation of this article the first author was supported by TÜBİTAK, the Scientific and Technological Research Council of Turkey, and the University of Siegen.

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Boylan, H., Skoruppa, NP. Explicit formulas for Hecke Gauss sums in quadratic number fields. Abh. Math. Semin. Univ. Hambg. 80, 213–226 (2010). https://doi.org/10.1007/s12188-010-0041-0

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  • DOI: https://doi.org/10.1007/s12188-010-0041-0

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