Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems
arXiv:1202.3965
Abstract
This paper is an expanded version of the author's lecture at the Integers Conference 2011. We discuss the secondary terms in the Davenport-Heilbronn theorems on cubic fields and 3-torsion in class groups of quadratic fields. Such secondary terms had been conjectured by Datskovsky-Wright and Roberts, and proofs of these or closely related secondary terms were obtained independently by Bhargava, Shankar, and Tsimerman; Hough; Zhao; and Taniguchi and the author. In this paper we discuss the history of the problem and highlight the diverse methods used to address it.
18 pages, survey/overview of recent work. To submit to the proceedings of Integers 2011 shortly. Comments very welcome!