Minimal index of bicyclic biquadratic number fields

Tímea Arnóczki; Gábor Nyul

doi:10.1216/rmj.2020.50.1

Abstract

T. Nakahara proved that the set of minimal indices of bicyclic biquadratic number fields with field index $1$ is unbounded. We strengthen his result by showing that this set just coincides with the set of positive integers, and every positive integer occurs infinitely many times as minimal index of totally complex bicyclic biquadratic number fields. Moreover, we study the analogous problem for all the other possible values of the field index.

Citation

Download Citation

Tímea Arnóczki. Gábor Nyul. "Minimal index of bicyclic biquadratic number fields." Rocky Mountain J. Math. 50 (1) 1 - 8, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.1

Information

Received: 30 January 2019; Revised: 17 July 2019; Accepted: 27 July 2019; Published: Febuary 2020

First available in Project Euclid: 30 April 2020

zbMATH: 07201550

MathSciNet: MR4092540

Digital Object Identifier: 10.1216/rmj.2020.50.1

Subjects:

Primary: 11D57 , 11R16

Keywords: bicyclic biquadratic number field , field index , minimal index

Abstract

Citation

Information

KEYWORDS/PHRASES

PUBLICATION TITLE:

PUBLICATION YEARS