The Euclidean algorithm on number fields and related problems

Speaker: Subramani Muthukrishnan (Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Tamil Nadu, India)
Abstract: The Euclidean Algorithm is a method for determining the greatest common divisor of two integers. In this talk, we will study the Euclidean algorithm for integral domains, particularly focusing on the ring of integers of an algebraic number field. Specifically, we will explore the Euclidean algorithm for abelian number fields of small degrees and the Euclidean algorithm for ideal classes. If time permits, we will also discuss some of our recent results on class numbers of quadratic number fields. This is joint work with K. Srinivas, Jaitra Chattopadhyay, and Usha K Sangale.