Explicit formulas for Hecke Gauss sums in quadratic number fields
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, cilt.80, sa.2, ss.213-226, 2010 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 80 Sayı: 2
- Basım Tarihi: 2010
- Doi Numarası: 10.1007/s12188-010-0041-0
- Dergi Adı: ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.213-226
- İstanbul Üniversitesi Adresli: Hayır
Özet
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.
We derive an explicit formula for Hecke-Gauss sums of quadratic
number fi elds. As an immediate consequence we obtain a quadratic reciprocity
law in quadratic number fi elds 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.