An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five

被引：2

作者：

Aoki, Miho ^{[1
]}

Kishi, Yasuhiro ^{[2
]}

机构：

[1] Shimane Univ, Interdisciplinary Fac Sci & Engn, Dept Math, Matsue, Shimane 6908504, Japan

[2] Aichi Univ Educ, Fac Educ, Dept Math, Kariya, Aichi 4488542, Japan

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 176卷

关键词：

Quadratic fields; Quartic fields; Class numbers;

D O I：

10.1016/j.jnt.2016.12.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a new infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five. Let n be a positive integer that satisfy n 3 (mod 500) and n not equivalent to 0 (mod 3). We prove that 5 divides the class numbers of both Q(root 2 - F-n) and Q(root 5(2 - F-n)) where Fn, is the nth Fibonacci number. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：333 / 343

页数：11

共 50 条

[31] Quadratic function fields whose class numbers are not divisible by three
Ichimura, H
ACTA ARITHMETICA, 1999, 91 (02) : 181 - 190
[32] Inequalities of Ono numbers and class numbers associated to imaginary quadratic fields
Shimizu, Kenichi
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2009, 85 (04) : 46 - 48
[33] CONSTRUCTION OF IMAGINARY QUADRATIC FIELDS WITH INFINITE CLASS FIELD TOWER
SCHMITHALS, B
ARCHIV DER MATHEMATIK, 1980, 34 (04) : 307 - 312
[34] Sum of three squares and class numbers of imaginary quadratic fields
Cho, Peter Jaehyun
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2011, 87 (06) : 91 - 94
[35] Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields
Kim, Kwang-Seob
MATHEMATICS, 2022, 10 (14)
[36] Averages and moments associated to class numbers of imaginary quadratic fields
Heath-Brown, D. R.
Pierce, L. B.
COMPOSITIO MATHEMATICA, 2017, 153 (11) : 2287 - 2309
[37] Dedekind sums with characters and class numbers of imaginary quadratic fields
Ota, K
ACTA ARITHMETICA, 2003, 108 (03) : 203 - 215
[38] QUADRATIC CLASS NUMBERS DIVISIBLE BY 3
Heath-Brown, Roger
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2007, 37 (01) : 203 - 211
[39] L-FUNCTIONS AND CLASS-NUMBERS OF IMAGINARY QUADRATIC FIELDS AND OF QUADRATIC EXTENSIONS OF AN IMAGINARY QUADRATIC FIELD
LOUBOUTIN, S
MATHEMATICS OF COMPUTATION, 1992, 59 (199) : 213 - 230
[40] Simultaneous indivisibility of class numbers of pairs of real quadratic fields
Chattopadhyay, Jaitra
Saikia, Anupam
RAMANUJAN JOURNAL, 2022, 58 (03): : 905 - 911

← 1 2 3 4 5 →