Counting Cubic Fields with Bounded Discriminant

摘要: In this talk, I will present the recent work of establishing the secondary terms of counting functions of cubic number fields or cubic function fields with bounded discriminant. These secondary terms had been conjectured by Datskovsky-Wright and Roberts, proofs of these were obtained independently by Bhargava, Shankar and Tsimerman, Taniguchi and Thorne for number fields and the speaker for function fields. In the first part of my talk I will give a friendly introduction on counting fields with small degree. This should be accessible to a general audience.