Ratios of the Ring Class Numbers and Class Numbers of a Real Quadratic Field

A. TARIQ, S. I. A. SHAH, A. ALI

Abstract


For a non-square integer n >1,let 𝐾=𝑸(√𝑛) be a real quadratic field. In this paper we prove the existence of a new family of infinitely many rings of conductors >1 whose ratios of ring class numbers and class numbers of K are divisible by a given power of 2 as an extension of our previous work. In addition, we extend the family in our previous work to a countable number of families, each consisting of infinitely many rings of conductors >1 such that the ratios for each successive family are exactly divisible by a progressively higher power of 2.

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Sindh University Research Journal - SURJ (Science Series)

 Copyright © University of Sindh, Jamshoro. 2017 All Rights Reserved.
Printing and Publication by: Sindh University Press.