Filtrations of units of Viète field-Reference-Cited by-同舟云学术

Filtrations of units of Viète field

Published:2019-12-26 Issue:05 Volume:16 Page:1067-1079
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Morisawa Takayuki¹,Okazaki Ryotaro²

Affiliation:

1. Division of Liberal Arts, Kogakuin University, 2665-1 Nakano, Hachioji, Tokyo 192-0015, Japan

2. Junior Division, College of Arts and Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8902, Japan

Abstract

Let [Formula: see text] be the [Formula: see text]th Viète field for any non-negative integer [Formula: see text]. We are interested in the relative unit group of [Formula: see text]. In this paper, we consider two filtrations of the relative unit group from Galois actions and from congruences and show that they are equal. And, as applications, we estimate the Mahler measure and the trace of square of relative units.

Funder

Japan Society for the Promotion of Science

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500554

Reference9 articles.

1. Weber's Class Number Problem in the Cyclotomic ℤ2-Extension of ℚ

2. Weber’s class number problem in the cyclotomic \mathbb{Z}_2-extension of \mathbb{Q}, II

3. WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ2-EXTENSION OF ℚ, III

4. Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field

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