GRADUATE SCHOOL OF SCIENCES & ENGINEERING
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
Rumeli Feneri Yolu
Thesis Committee Members:
Assoc. Prof. Kazım Büyükboduk (Advisor, Koç University)
Prof. Tolga Etgü (Koç University)
Assoc. Prof. Ayhan Günaydın (Boğaziçi University)
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.