Multivariate Lucas polynomials and ideal classes in quadratic number fields


ZEYTİN A.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.4, pp.1543-1555, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1608-65
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1543-1555

Abstract

In this work, by using Pauli matrices, we introduce four families of polynomials indexed over the positive integers. These polynomials have rational or imaginary rational coefficients. It turns out that two of these families are closely related to classical Lucas and Fibonacci polynomial sequences and hence to Lucas and Fibonacci numbers. We use one of these families to give a geometric interpretation of the 200-year-old class number problems of Gau beta, which is equivalent to the study of narrow ideal classes in real quadratic number fields.