CHARACTERIZATION OF NORM FORMS VIA THEIR VALUES AT INTEGER POINTS

被引：0

作者：

Tomanov, George ^{[1
]}

机构：

[1] Univ Claude Bernard Lyon I, Inst Camille Jordan, Batiment Math,43 Bld 11 Novembre 1918, F-69622 Villeurbanne, France

来源：

JOURNAL OF MODERN DYNAMICS | 2024年 / 20卷

关键词：

Homogeneous spaces; real algebraic groups defined over the rational numbers; norm forms; values of forms at integer points; ORBITS; TORI;

D O I：

10.3934/jmd.2024018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. Using a homogeneous dynamics approach, we obtain a complete description of the forms with discrete set of values at integer points and not representing zero over the rational numbers non-trivially. It turns out that these are exactly the norm forms and the quasi-norm forms (introduced in the paper). As a by-product, we obtain a general class of non-totally real forms for which a natural generalization of the conjecture of Cassels and SwinnertonDyer fails.

引用

页码：663 / 678

页数：16

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