ON RELATIVE CLASS NUMBER AND CONTINUED FRACTIONS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 5, 2015, pp.1559-1568
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.5.1559

Title & Authors

ON RELATIVE CLASS NUMBER AND CONTINUED FRACTIONS

CHAKRABORTY, DEBOPAM; SAIKIA, ANUPAM;

CHAKRABORTY, DEBOPAM; SAIKIA, ANUPAM;

Abstract

The relative class number of a real quadratic field of discriminant d is the ratio of class numbers of and , where denotes the ring of integers of K and is the order of conductor f given by . In a recent paper of A. Furness and E. A. Parker the relative class number of has been investigated using continued fraction in the special case when has a diagonal form. Here, we extend their result and show that there exists a conductor f of relative class number 1 when the continued fraction of is non-diagonal of period 4 or 5. We also show that there exist infinitely many real quadratic fields with any power of 2 as relative class number if there are infinitely many Mersenne primes.

Keywords

relative class number;continued fraction;

Language

English

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