Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
205-212
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-03
poprawiono
1997-05-14
Twórcy
autor
- Département de Mathématiques, Université de Caen, UFR Sciences 14032 Caen Cedex, France
Bibliografia
- [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 $\vert L(1,χ )\vert$, 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.
- [Lou 4] S. Louboutin, A finiteness theorem for imaginary abelian number fields, Manuscripta Math. 91 (1996), 343-352.
- [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.
- [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140.
- [Miy] I. Miyada, On imaginary abelian number fields of type $(2,2,\dots, 2)$ with one class in each genus, Manuscripta Math. 88 (1995), 535-540.
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv75z2p205bwm