Multivariate Lucas polynomials and ideal classes in quadratic number fields

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ZEYTİN A.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.4, ss.1543-1555, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1608-65
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1543-1555
  • Galatasaray Üniversitesi Adresli: Evet

Özet

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.