Geometry-of-numbers methods in the cusp

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2025-05-14 DOI:10.2140/ant.2025.19.1099

Arul Shankar, Artane Siad, Ashvin A. Swaminathan, Ila Varma

引用次数: 0

Abstract

We develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal interest in number theory, namely that of the split orthogonal group acting on the space of quadratic forms.

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尖端的数的几何方法

我们开发了新的方法来计算具有有界不变量的积分轨道，这些不变量位于共正则表示的基本域的尖端内。我们举例说明这些方法的主要兴趣在数论的表示，即分裂正交群作用于二次型的空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.