Shintani cones for complex cubic number fields

Author:

Capuñay Alex1

Affiliation:

1. Departamento de Matemática, Facultad de Ciencias, Universidad de Chile, Santiago, Las Palmeras #3425, Ñuñoa 7800003, Chile

Abstract

In 1979, Shintani showed the existence of a fundamental domain, consisting of a finite number of [Formula: see text]-rational polyhedral cones, for the action of the units of a number field [Formula: see text] under its geometric embedding. Explicit construction of such cones is only known for totally real fields of degree [Formula: see text]. Here, we extend this to complex cubic fields using Espinoza’s work on signed Shintani domains for such fields.

Funder

ANID-CHILE BECA NACIONAL DE DOCTORADO

Chilean FONDECYT

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Attractor-repeller construction of Shintani domains for totally complex quartic fields;Journal of Number Theory;2024-05

2. Computing Shintani domains;International Journal of Number Theory;2023-11-21

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