CLASS NUMBER ONE CRITERION FOR SOME NON-NORMAL TOTALLY REAL CUBIC FIELDS

Let {Km } m≥4be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomialfm (x) =x 3−mx 2− (m+ 1)x− 1, wheremis an integer withm≥ 4. In this paper, we will give a class number one criterion forKm . 2010Mathematics Subject Classification: Primary 11R42; Sec...

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Published inTaiwanese journal of mathematics Vol. 17; no. 3; pp. 981 - 989
Main Author Lee, Jun Ho
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2013
Subjects
Mathematical functions
Polynomials
Prime numbers
Online AccessGet full text
ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.17.2013.2424

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Abstract Let {Km } m≥4be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomialfm (x) =x 3−mx 2− (m+ 1)x− 1, wheremis an integer withm≥ 4. In this paper, we will give a class number one criterion forKm . 2010Mathematics Subject Classification: Primary 11R42; Secondary 11R16, 11R29. Key words and phrases: Cubic fields, Class number, Zeta function.
AbstractList Let {Km } m≥4be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomialfm (x) =x 3−mx 2− (m+ 1)x− 1, wheremis an integer withm≥ 4. In this paper, we will give a class number one criterion forKm . 2010Mathematics Subject Classification: Primary 11R42; Secondary 11R16, 11R29. Key words and phrases: Cubic fields, Class number, Zeta function.
Author Lee, Jun Ho
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Cites_doi 10.1017/S0027763000007741
10.1007/s229-001-8025-7
10.3792/pjaa.74.13
10.1007/s00229-007-0135-x
10.1016/0022-314X(90)90090-E
10.1017/S0027763000001185
10.1006/jnth.1996.0052
10.1006/jnth.1997.2059
10.1515/crll.1913.142.153
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Snippet Let {Km } m≥4be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomialfm (x) =x 3−mx 2− (m+ 1)x− 1, wheremis an...
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SubjectTerms Mathematical functions
Polynomials
Prime numbers
Title CLASS NUMBER ONE CRITERION FOR SOME NON-NORMAL TOTALLY REAL CUBIC FIELDS
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