Exponent of class group of certain imaginary quadratic fields

Kalyan Chakraborty; Azizul Hoque

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 4, page 1167-1178
  • ISSN: 0011-4642

Abstract

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Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form ℚ x 2 - 2 y n whose ideal class group has an element of order n . This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.

How to cite

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Chakraborty, Kalyan, and Hoque, Azizul. "Exponent of class group of certain imaginary quadratic fields." Czechoslovak Mathematical Journal 70.4 (2020): 1167-1178. <http://eudml.org/doc/296954>.

@article{Chakraborty2020,
abstract = {Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb \{Q\} \bigl (\sqrt\{x^2-2y^n\} \bigr )$ whose ideal class group has an element of order $n$. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.},
author = {Chakraborty, Kalyan, Hoque, Azizul},
journal = {Czechoslovak Mathematical Journal},
keywords = {quadratic field; discriminant; class group; Wada's conjecture},
language = {eng},
number = {4},
pages = {1167-1178},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Exponent of class group of certain imaginary quadratic fields},
url = {http://eudml.org/doc/296954},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Chakraborty, Kalyan
AU - Hoque, Azizul
TI - Exponent of class group of certain imaginary quadratic fields
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 1167
EP - 1178
AB - Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb {Q} \bigl (\sqrt{x^2-2y^n} \bigr )$ whose ideal class group has an element of order $n$. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
LA - eng
KW - quadratic field; discriminant; class group; Wada's conjecture
UR - http://eudml.org/doc/296954
ER -

References

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