Universal quadratic forms and indecomposables in number fields: A survey

Vítězslav Kala

Type: Article

Publication Date: 2023-07-17

Citations: 4

DOI: https://doi.org/10.46298/cm.10896

Abstract

We give an overview of universal quadratic forms and lattices, focusing on the recent developments over the rings of integers in totally real number fields. In particular, we discuss indecomposable algebraic integers as one of the main tools.

Locations

Communications in Mathematics - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (83)

Action	Title	Year	Authors
+	Berechnung von Zetafunktionen an ganzzahligen Stellen	1979	Carl Ludwig Siegel K. Chandrasekharan H. Maaß
+	A refinement of the Dress–Scharlau theorem	2015	Se Wook Jang Byeong Moon Kim
+	Representations of positive definite quadratic forms.	1978	Martin Kneser Yoshiyuki Kitaoka J. S. Hsia
+	Some recent results about (ternary) quadratic forms	2004	Jonathan Hanke
+ PDF Chat	Universal octonary diagonal forms over some real quadratic fields	2000	B. M. Kim
+ PDF Chat	Universal binary Hermitian forms	1997	A. G. Earnest Azar Khosravani
+	Representations of Positive Definite Senary Integral Quadratic Forms by a Sum of Squares	1997	Myung-Hwan Kim Byeong-Kweon Oh
+	ON THE REPRESENTATION OF A QUADRATIC FORM AS A SUM OF SQUARES OF LINEAR FORMS	1937	Chao Ko
+ PDF Chat	Determination of all classes of positive quaternary quadratic forms which represent all (positive) integers	1948	Margaret F. Willerding
+	Binary quadratic forms represented by a sum of nonzero squares	2014	Yun-Seong Ji Myung-Hwan Kim Byeong-Kweon Oh