On the Davenport-Heilbronn theorem and second order terms

Details On the Davenport-Heilbronn theorem and second order terms On the Davenport-Heilbronn theorem and second order terms

2010-05-05

arxiv.org/abs/1005.0672v2

Mathematics

Number Theory

33 pages

Scientific paper

We give a simple proof of the Davenport--Heilbronn theorem which gives the main term in the asymptotics for the number of cubic fields having bounded discriminant. We also prove a conjecture of Roberts which gives the second main term in the latter theorem. Our arguments provide natural interpretations for the constants appearing in these theorems in terms of local masses of cubic rings.

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