On the class number of the maximal real subfields of a family of cyclotomic fields

Ram, Mahesh Kumar. "On the class number of the maximal real subfields of a family of cyclotomic fields." Czechoslovak Mathematical Journal 73.3 (2023): 937-940. <http://eudml.org/doc/299123>.

@article{Ram2023,
abstract = {For any square-free positive integer $m\equiv \{10\}\hspace\{4.44443pt\}(\@mod \; 16)$ with $m\ge 26$, we prove that the class number of the real cyclotomic field $\mathbb \{Q\}(\zeta _\{4m\}+\zeta _\{4m\}^\{-1\})$ is greater than $1$, where $\zeta _\{4m\}$ is a primitive $4m$th root of unity.},
author = {Ram, Mahesh Kumar},
journal = {Czechoslovak Mathematical Journal},
keywords = {maximal real subfield of cyclotomic field; real quadratic field; class number},
language = {eng},
number = {3},
pages = {937-940},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the class number of the maximal real subfields of a family of cyclotomic fields},
url = {http://eudml.org/doc/299123},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Ram, Mahesh Kumar
TI - On the class number of the maximal real subfields of a family of cyclotomic fields
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 937
EP - 940
AB - For any square-free positive integer $m\equiv {10}\hspace{4.44443pt}(\@mod \; 16)$ with $m\ge 26$, we prove that the class number of the real cyclotomic field $\mathbb {Q}(\zeta _{4m}+\zeta _{4m}^{-1})$ is greater than $1$, where $\zeta _{4m}$ is a primitive $4m$th root of unity.
LA - eng
KW - maximal real subfield of cyclotomic field; real quadratic field; class number
UR - http://eudml.org/doc/299123
ER -