English

Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems

Number Theory 2012-02-20 v1

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.

Keywords

Cite

@article{arxiv.1202.3965,
  title  = {Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems},
  author = {Frank Thorne},
  journal= {arXiv preprint arXiv:1202.3965},
  year   = {2012}
}

Comments

18 pages, survey/overview of recent work. To submit to the proceedings of Integers 2011 shortly. Comments very welcome!