On Dirichlet biquadratic fields

被引：0

作者：

Fouvry, Etienne ^{[1
]}

Koymans, Peter ^{[2
]}

机构：

[1] Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France

[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2022年 / 34卷 / 03期

关键词：

NUMBER; HEURISTICS;

D O I：

10.5802/jtnb.1220

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of a subset, with positive natural density, of squarefree integers n > 0such that the4-rank of the ideal class group of Q(root-n, root n)is omega(3)(n)-1, where omega(3)(n)is the number of prime divisors of n that are3modulo4. Recall that for the class groups associated to Q(root n) or Q(root-n)an analogous subset of n does not exist

引用

页码：637 / 646

页数：11

共 50 条

[31] Chatelain’s integer bases for biquadratic fields
Tanoé F.E.
Afrika Matematika, 2017, 28 (5-6) : 727 - 744
[32] ON CYCLIC BIQUADRATIC FIELDS RELATED TO A PROBLEM OF HASSE
NAKAHARA, T
MONATSHEFTE FUR MATHEMATIK, 1982, 94 (02): : 125 - 132
[33] TRUNCATED UNITS FOR BIQUADRATIC AND BICUBIC NUMBER FIELDS
STENDER, HJ
MATHEMATISCHE ANNALEN, 1978, 232 (01) : 55 - 64
[34] UNITY IN PRIMITIVE BIQUADRATIC FIELDS OF FIRST ORDER
NAGELL, T
ARKIV FOR MATEMATIK, 1968, 7 (04): : 359 - &
[35] Universal quadratic forms and indecomposables over biquadratic fields
Cech, Martin
Lachman, Dominik
Svoboda, Josef
Tinkova, Magdalena
Zemkova, Kristysma
MATHEMATISCHE NACHRICHTEN, 2019, 292 (03) : 540 - 555
[36] On the odd part of tame kernels of biquadratic number fields
Zhou, Haiyan
ACTA ARITHMETICA, 2010, 144 (03) : 275 - 286
[37] POWER INTEGRAL BASES IN PARAMETRIC FAMILIES OF BIQUADRATIC FIELDS
Gaal, Istvan
Szabo, Timea
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2012, 24 (01): : 105 - 114
[38] An explicit construction for unramified quadratic extensions of biquadratic fields
Chakraborty, Debopam
Saikia, Anupam
ACTA ARITHMETICA, 2017, 178 (02) : 153 - 161
[39] The extended Bloch groups of biquadratic and dihedral number fields
Guo, Xuejun
Qin, Hourong
JOURNAL OF PURE AND APPLIED ALGEBRA, 2018, 222 (12) : 3968 - 3981
[40] On Greenberg's conjecture for certain real biquadratic fields
El Mahi, Abdelakder
Ziane, M'hammed
PERIODICA MATHEMATICA HUNGARICA, 2024, 88 (02) : 475 - 483

← 1 2 3 4 5 →