# A determinant formula for the relative class number of an imaginary abelian number field

Communications in Mathematics (2014)

- Volume: 22, Issue: 2, page 133-140
- ISSN: 1804-1388

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topHirabayashi, Mikihito. "A determinant formula for the relative class number of an imaginary abelian number field." Communications in Mathematics 22.2 (2014): 133-140. <http://eudml.org/doc/269863>.

@article{Hirabayashi2014,

abstract = {We give a new formula for the relative class number of an imaginary abelian number field $K$ by means of determinant with elements being integers of a cyclotomic field generated by the values of an odd Dirichlet character associated to $K$. We prove it by a specialization of determinant formula of Hasse.},

author = {Hirabayashi, Mikihito},

journal = {Communications in Mathematics},

keywords = {imaginary abelian number field; relative class number; determinant; class number formula; imaginary abelian number field; relative class number; determinant; class number formula},

language = {eng},

number = {2},

pages = {133-140},

publisher = {University of Ostrava},

title = {A determinant formula for the relative class number of an imaginary abelian number field},

url = {http://eudml.org/doc/269863},

volume = {22},

year = {2014},

}

TY - JOUR

AU - Hirabayashi, Mikihito

TI - A determinant formula for the relative class number of an imaginary abelian number field

JO - Communications in Mathematics

PY - 2014

PB - University of Ostrava

VL - 22

IS - 2

SP - 133

EP - 140

AB - We give a new formula for the relative class number of an imaginary abelian number field $K$ by means of determinant with elements being integers of a cyclotomic field generated by the values of an odd Dirichlet character associated to $K$. We prove it by a specialization of determinant formula of Hasse.

LA - eng

KW - imaginary abelian number field; relative class number; determinant; class number formula; imaginary abelian number field; relative class number; determinant; class number formula

UR - http://eudml.org/doc/269863

ER -

## References

top- Girstmair, K., The relative class numbers of imaginary cyclic fields of degrees 4, 6, 8 and 10, Math. Comp., 61, 1993, 881-887, (1993) Zbl0787.11046MR1195428
- Hasse, H., Über die Klassenzahl abelscher Zahlkörper, 1952, Akademie-Verlag, Berlin, Reprinted with an introduction by J. Martinet, Springer Verlag, Berlin (1985). (1952) Zbl0046.26003MR0842666
- Hirabayashi, M., Yoshino, K., 10.1007/BF01258662, Manuscripta math., 60, 1988, 423-436, (1988) Zbl0654.12002MR0933473DOI10.1007/BF01258662
- Washington, L.C., Introduction to Cyclotomic Fields, 2nd edition, 1997, Springer Verlag, Berlin, (1997) MR1421575
- Yamamura, K., Bibliography on determinantal expressions of relative class numbers of imaginary abelian number fields, Number Theory. Dreaming in Dreams. Proceedings of the 5th China-Japan Seminar, 2010, 244-250, World Sci. Publ., Hackensack, (2010) Zbl1202.11001MR2798466

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