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}
}
  • Takashi Taniguchi, F. Thorne
  • Published 2011
  • Mathematics
  • arXiv: Number Theory
  • 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
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