A note on the class number of certain real cyclotomic fields

被引:0
作者
Prakash, Om [1 ]
机构
[1] Kerala Sch Math, Kozhikode 673571, Kerala, India
关键词
Diophantine equation; Continued fraction; Class number; Quadratic field; Real cyclotomic field; SUBFIELD;
D O I
10.1007/s13226-024-00544-0
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes some results of [6] in the sense that our family includes theirs.
引用
收藏
页数:6
相关论文
共 9 条
[1]  
ANKENY NC, 1965, J REINE ANGEW MATH, V217, P217
[2]   DISTRIBUTION OF CLASS NUMBERS IN CONTINUED FRACTION FAMILIES OF REAL QUADRATIC FIELDS [J].
Dahl, Alexander ;
Kala, Vitezslav .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2018, 61 (04) :1193-1212
[3]   Pell-type equations and class number of the maximal real subfield of a cyclotomic field [J].
Hoque, Azizul ;
Chakraborty, Kalyan .
RAMANUJAN JOURNAL, 2018, 46 (03) :727-742
[4]   ON THE CLASS-NUMBER OF THE MAXIMAL REAL SUBFIELD OF A CYCLOTOMIC FIELD [J].
Hoque, Azizul ;
Saikia, Helen K. .
Quaestiones Mathematicae, 2016, 39 (07) :889-894
[5]  
LANG SD, 1977, J REINE ANGEW MATH, V290, P70
[6]   Class numbers of totally real fields and applications to the Weber class number problem [J].
Miller, John C. .
ACTA ARITHMETICA, 2014, 164 (04) :381-397
[7]   Class groups of real cyclotomic fields [J].
Mishra, Mohit ;
Schoof, Rene ;
Washington, Lawrence C. .
MONATSHEFTE FUR MATHEMATIK, 2021, 195 (03) :489-496
[9]  
YAMAGUCHI I, 1975, J REINE ANGEW MATH, V272, P217