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The class number one problem for some non-normal CM-fields of degree 2p

✍ Scribed by Jeoung-Hwan Ahn; Gérard Boutteaux; Soun-Hi Kwon; Stéphane Louboutin

Book ID
113731156
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
224 KB
Volume
132
Category
Article
ISSN
0022-314X

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It is known that if we assume the Generalized Riemann Hypothesis, then any normal CM-field with relative class number one is of degree less than or equal to 96. All normal CM-fields of degree less than 48 with class number one are known. In addition, for normal CM-fields of degree 48 the class numbe

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✍ Stéphane R. Louboutin 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 136 KB

We prove that there are effectively only finitely many real cubic number fields of a given class number with negative discriminants and ring of algebraic integers generated by an algebraic unit. As an example, we then determine all these cubic number fields of class number one. There are 42 of them.