Composition of binary quadratic forms over number fields-Reference-Cited by-同舟云学术

Composition of binary quadratic forms over number fields

Published:2021-12-01 Issue:6 Volume:71 Page:1339-1360
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Zemková Kristýna¹²

Affiliation:

1. Charles University, Faculty of Mathematics and Physics , Department of Algebra , Sokolovská , 83, 18600 Praha 8 , Czech Republic

2. Fakultät für Mathematik, Technische Universität Dortmund , D-44221 , Dortmund , Germany

Abstract

Abstract In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one. The article contains an explicit description of the correspondence. In the case of totally negative discriminants, equivalent conditions are given for a binary quadratic form to be totally positive definite.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2021-0057/pdf

Reference24 articles.

1. Bhargava, M.: Higher composition laws I: A new view on Gauss composition, and quadratic generalizations, Ann. of Math. 159 (2004), 217–250.

2. Blomer, V.—Kala, V.: Number fields without n-ary universal quadratic forms, Math. Proc. Cambridge Philos. Soc. 159(2) (2015), 239–252.

3. Blomer, V.—Kala, V.: On the rank of universal quadratic forms over real quadratic fields, Doc. Math. 23 (2018), 15–34.

4. Butts, H.—Dulin, B.: Composition of binary quadratic forms over integral domains, Acta Arith. 20(3) (1972), 223–251.

5. Butts, H.—Estes, D.: Modules and binary quadratic forms over integral domains, Linear Algebra App. 1(2) (1968), 153–180.

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