Ayberk ZEYTİN

8897

Multivariate Lucas polynomials and ideal classes in quadratic number fields

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 Gauß, which is equivalent to the study of narrow ideal classes in real quadratic number fields.

Keywords:

Pauli matrices, Fibonacci polynomials, Lucas polynomials, çarks, çark hypersurfaces, indefinite binary quadratic forms, class number problems of Gauß, real quadratic number fields narrow ideal classes,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

Sayıdaki Diğer Makaleler

Ali Reza Moniri HAMZEKOLAEE, Abdullah HARMANCI, Yahya TALEBI, Burcu ÜNGÖR

Arif SALIMOV, Habil FATTAEV

Fatma ATEŞ, Erdem KOCAKUŞAKLI, İsmail GÖK, Yusuf YAYLI

Ramazan AKGÜN, Arash GHORBANALIZADEH

Miroslav DOUPOVEC, Jan KUREK, Wlodzimierz MIKULSKI

On the global L p boundedness of a general class of h-Fourier integral operators

Chafika Amel AITEMRAR, Abderrahmane SENOUSSAOUI

Subuhi KHAN, Shahid Ahmad WANI

Niovi KEHAYOPULU

A study of the tubular surfaces constructed by the spherical indicatrices in Euclidean 3−space

Yusuf YAYLI, Fatma ATEŞ, Erdem KOCAKUŞAKLI, İsmail GÖK