On the Relative Class Number of the Imaginary Abelian Number Field II

On the Class Number of Abelian Number Fields ◽

10.1007/978-3-030-01512-1_5 ◽

2019 ◽

pp. 307-357

Author(s):

Helmut Hasse

Keyword(s):

Number Field ◽

Class Number ◽

Relative Class ◽

Relative Class Number ◽

Abelian Number Field

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On the Relative Class Number of the Imaginary Abelian Number Field I

On the Class Number of Abelian Number Fields ◽

10.1007/978-3-030-01512-1_4 ◽

2019 ◽

pp. 255-305

Author(s):

Helmut Hasse

Keyword(s):

Number Field ◽

Class Number ◽

Relative Class ◽

Relative Class Number ◽

Abelian Number Field

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A relative class number formula for an imaginary abelian number field by means of Dedekind sum

manuscripta mathematica ◽

10.1007/s00229-002-0304-x ◽

2002 ◽

Vol 109 (2) ◽

pp. 223-227 ◽

Author(s):

Mikihito Hirabayashi

Keyword(s):

Number Field ◽

Class Number ◽

Dedekind Sum ◽

Relative Class ◽

Class Number Formula ◽

Relative Class Number ◽

Number Formula ◽

Abelian Number Field

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An index formula for the relative class number of an abelian number field

Journal of Number Theory ◽

10.1016/0022-314x(89)90100-5 ◽

1989 ◽

Vol 32 (1) ◽

pp. 100-110 ◽

Author(s):

Kurt Girstmair

Keyword(s):

Number Field ◽

Class Number ◽

Index Formula ◽

Relative Class ◽

Relative Class Number ◽

Abelian Number Field

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On an index formula for the relative class number of a cyclotomic number field

Journal of Number Theory ◽

10.1016/0022-314x(90)90094-8 ◽

1990 ◽

Vol 36 (3) ◽

pp. 332-338

Author(s):

Akira Endô

Keyword(s):

Number Field ◽

Class Number ◽

Index Formula ◽

Cyclotomic Number ◽

Relative Class ◽

Relative Class Number

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On the relative class number of a relative Galois number field

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/02440552 ◽

1972 ◽

Vol 24 (4) ◽

pp. 552-557

Author(s):

Kiichiro OHTA

Keyword(s):

Number Field ◽

Class Number ◽

Relative Class ◽

Relative Class Number ◽

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Another look at real quadratic fields of relative class number 1

Acta Arithmetica ◽

10.4064/aa163-4-5 ◽

2014 ◽

Vol 163 (4) ◽

pp. 371-377 ◽

Author(s):

Debopam Chakraborty ◽

Anupam Saikia

Keyword(s):

Class Number ◽

Quadratic Fields ◽

Real Quadratic Fields ◽

Relative Class ◽

Relative Class Number ◽

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On Dirichletʼs conjecture on relative class number one

Journal of Number Theory ◽

10.1016/j.jnt.2012.01.009 ◽

2012 ◽

Vol 132 (7) ◽

pp. 1398-1403 ◽

Author(s):

Amanda Furness ◽

Adam E. Parker

Keyword(s):

Class Number ◽

Relative Class ◽

Relative Class Number

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The Non-normal Quartic CM-Fields and the Octic Dihedral CM-Fields with Relative Class Number Two

Journal of Number Theory ◽

10.1006/jnth.1999.2421 ◽

1999 ◽

Vol 79 (2) ◽

pp. 175-193 ◽

Author(s):

Hee-Sun Yang ◽

Soun-Hi Kwon

Keyword(s):

Class Number ◽

Relative Class ◽

Relative Class Number

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On the Stickelberger ideal and the relative class number

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1987-0891643-8 ◽

1987 ◽

Vol 302 (2) ◽

pp. 727-727 ◽

Author(s):

Tatsuo Kimura ◽

Kuniaki Horie

Keyword(s):

Class Number ◽

Relative Class ◽

Relative Class Number ◽

Stickelberger Ideal

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A Generalization of Jakubec's Formula

Mathematica Slovaca ◽

10.1515/ms-2015-0018 ◽

2015 ◽

Vol 65 (1) ◽

Author(s):

Mikihito Hirabayashi

Keyword(s):

Class Number ◽

Cyclotomic Field ◽

Not Given ◽

Relative Class ◽

Relative Class Number

AbstractIn 2009 Jakubec gave two determinantal formulas for the relative class number of the pth cyclotomic field, p an odd prime. We generalize one of the formulas to an arbitrary cyclotomic field and also determine the sign of the formula, which he had not given.

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