Class Numbers of Certain Quadratic Fields

Speaker: 
Kalyan Chakraborty
Date: 
Thu, Jul 5, 2018
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 
Class number of a number field is one of the fundamental and mysterious objects in algebraic number theory and related topics. I will discuss the class numbers of some quadratic fields. More precisely, I will discuss some results concerning the divisibility of the class numbers of certain families of real (respectively, imaginary) quadratic fields in both qualitative and quantitative aspects. I will also look at the 3-rank of the ideal class groups of certain imaginary quadratic fields. The talk will be based on some recent works done along with my collaborators.