KOÇ UNIVERSITY
GRADUATE SCHOOL OF SCIENCES & ENGINEERING
MATHEMATICS
MS THESIS DEFENSE BY ÇAĞATAY ALTUNTAŞ
Title: Dedekind Zeta Function and Class Number Formula.
Speaker: Çağatay Altuntaş
Time: August 28, 2018, 17:00
Place: ENG 208
Koç University
Rumeli Feneri Yolu
Sariyer, Istanbul
Thesis Committee Members:
Assoc. Prof. Kazım Büyükboduk (Advisor, Koç University)
Prof. Tolga Etgü (Koç University)
Assoc. Prof. Ayhan Günaydın (Boğaziçi University)
Abstract:
In this thesis, we first introduce number fields and their ring of integers. We first show that the ring of integers of a number field is a Dedekind Domain. To study number fields in details, we present a geometric approach and show that the class number of a number field is finite and characterize the group of units of a ring of integers. After that, we introduce the Dedekind zeta function of a number field. Moreover, we present the Analytic Class Number Formula which states that the Dedekind zeta function converges for any complex number with real part greater than 1 and has a simple pole at the point 1. We show that its residue at 1 is given by particular invariants of a number field. Lastly, we present various arguments to evaluate class number of number fields.