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

Stéphane Louboutin

Colloquium Mathematicae (1998)

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

Abstract

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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.

How to cite

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Louboutin, 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

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  2. [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. 
  3. [Lou 2] S. Louboutin, Majorations explicites de | L ( 1 , χ ) | , C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 11-14. 
  4. [Lou 3] S. Louboutin, Lower bounds for relative class numbers of CM-fields, Proc. Amer. Math. Soc. 120 (1994), 425-434. Zbl0795.11058
  5. [Lou 4] S. Louboutin, A finiteness theorem for imaginary abelian number fields, Manuscripta Math. 91 (1996), 343-352. Zbl0869.11089
  6. [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
  7. [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140. Zbl0207.05602
  8. [Miy] I. Miyada, On imaginary abelian number fields of type ( 2 , 2 , , 2 ) with one class in each genus, Manuscripta Math. 88 (1995), 535-540. Zbl0851.11061
  9. [PK] Y.-H. Park and S.-H. Kwon, Determination of all imaginary abelian sextic number fields with class number 11 , Acta Arith., to appear. 
  10. [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982. 
  11. [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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