WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ2-EXTENSION OF ℚ, III-Reference-Cited by-同舟云学术

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

Published:2011-09 Issue:06 Volume:07 Page:1627-1635
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

FUKUDA TAKASHI¹,KOMATSU KEIICHI²

Affiliation:

1. Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan

2. Department of Mathematical Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan

Abstract

Let hn denote the class number of [Formula: see text] which is a cyclic extension of degree 2n over the rational number field ℚ. There are no known examples of hn > 1. We prove that a prime number ℓ does not divide hn for all n ≥ 1 if ℓ is less than 109 or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042111004782

Reference14 articles.

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2. A numerical study of Weber's real class number calculation

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

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

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