# Secondary terms in counting functions for cubic fields

@article{Taniguchi2011SecondaryTI, title={Secondary terms in counting functions for cubic fields}, author={Takashi Taniguchi and F. Thorne}, journal={arXiv: Number Theory}, year={2011} }

We prove the existence of secondary terms of order X^{5/6} in the Davenport-Heilbronn theorems on cubic fields and 3-torsion in class groups of quadratic fields. For cubic fields this confirms a conjecture of Datskovsky-Wright and Roberts. We also prove a variety of generalizations, including to arithmetic progressions, where we discover a curious bias in the secondary term. Roberts' conjecture has also been proved independently by Bhargava, Shankar, and Tsimerman. In contrast to their work… CONTINUE READING

55 Citations

Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems

- Computer Science, Mathematics
- 2012

3

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 57 REFERENCES