Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems

Details Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems

2012-02-17

arxiv.org/abs/1202.3965v1

Mathematics

Number Theory

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

Scientific paper

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.

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