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- Title
On Gauss sums over Dedekind domains.
- Authors
Zheng, Zhiyong; Chen, Man; Xu, Jie
- Abstract
It is a difficult question to generalize Gauss sums to a ring of algebraic integers of an arbitrary algebraic number field. In this paper, we define and discuss Gauss sums over a Dedekind domain of finite norm. In particular, we give a Davenport–Hasse type formula for some special Gauss sums. As an application, we give some more precise formulas for Gauss sums over the algebraic integer ring of an algebraic number field (see Theorems 4.1 and 4.2).
- Subjects
DEDEKIND sums; ALGEBRAIC numbers; RINGS of integers; RING theory; ALGEBRAIC fields; GAUSSIAN sums
- Publication
International Journal of Number Theory, 2022, Vol 18, Issue 5, p1047
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042122500543