# The imaginary cyclic sextic fields with class numbers equal to their genus class numbers

Colloquium Mathematicae (1998)

- Volume: 75, Issue: 2, page 205-212
- ISSN: 0010-1354

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topLouboutin, Stéphane. "The imaginary cyclic sextic fields with class numbers equal to their genus class numbers." Colloquium Mathematicae 75.2 (1998): 205-212. <http://eudml.org/doc/210539>.

@article{Louboutin1998,

abstract = {It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.},

author = {Louboutin, Stéphane},

journal = {Colloquium Mathematicae},

keywords = {relative class number; class number; genus field; sextic number field; genus class numbers; relative class numbers; imaginary cyclic sextic fields},

language = {eng},

number = {2},

pages = {205-212},

title = {The imaginary cyclic sextic fields with class numbers equal to their genus class numbers},

url = {http://eudml.org/doc/210539},

volume = {75},

year = {1998},

}

TY - JOUR

AU - Louboutin, Stéphane

TI - The imaginary cyclic sextic fields with class numbers equal to their genus class numbers

JO - Colloquium Mathematicae

PY - 1998

VL - 75

IS - 2

SP - 205

EP - 212

AB - It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.

LA - eng

KW - relative class number; class number; genus field; sextic number field; genus class numbers; relative class numbers; imaginary cyclic sextic fields

UR - http://eudml.org/doc/210539

ER -

## References

top- [Gra] M. N. Gras, Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de $Q$, J. Reine Angew. Math. 277 (1975), 89-116.
- [Lou 1] S. Louboutin, Minoration au point 1 des fonctions $L$ et détermination des corps sextiques abéliens totalement imaginaires principaux, Acta Arith. 62 (1992), 109-124.
- [Lou 2] S. Louboutin, Majorations explicites de $\left|L\right(1,\chi \left)\right|$, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 11-14.
- [Lou 3] S. Louboutin, Lower bounds for relative class numbers of CM-fields, Proc. Amer. Math. Soc. 120 (1994), 425-434. Zbl0795.11058
- [Lou 4] S. Louboutin, A finiteness theorem for imaginary abelian number fields, Manuscripta Math. 91 (1996), 343-352. Zbl0869.11089
- [Lou 5] S. Louboutin, The nonquadratic imaginary cyclic fields of $2$-power degrees with class numbers equal to their genus numbers, Proc. Amer. Math. Soc., to appear. Zbl0919.11071
- [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140. Zbl0207.05602
- [Miy] I. Miyada, On imaginary abelian number fields of type $(2,2,\cdots ,2)$ with one class in each genus, Manuscripta Math. 88 (1995), 535-540. Zbl0851.11061
- [PK] Y.-H. Park and S.-H. Kwon, Determination of all imaginary abelian sextic number fields with class number $\le 11$, Acta Arith., to appear.
- [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982.
- [Yam] K. Yamamura, The determination of the imaginary abelian number fields with class-number one, Math. Comp. 62 (1994), 899-921. Zbl0798.11046

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