Explicit formulas for Hecke Gauss sums in quadratic number fields

Autor:	Nils-Peter Skoruppa, Hatice Boylan
Rok vydání:	2010
Předmět:	Algebra symbols.namesake Number theory General Mathematics Gauss sum symbols Binary quadratic form Quadratic reciprocity Algebraic number field Quadratic Gauss sum Legendre symbol Quadratic residuosity problem Mathematics
Zdroj:	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. 80:213-226
ISSN:	1865-8784 0025-5858
DOI:	10.1007/s12188-010-0041-0
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2e53f8d95d05f5f5a628374cc5f813b4 https://doi.org/10.1007/s12188-010-0041-0 Zobrazit plný text záznamu Full text from SpringerLink