The 3-part of class numbers of quadratic fields
Publication
, Journal Article
Pierce, LB
Published in: Journal of the London Mathematical Society
2005
It is proved that the 3-part of the class number of a quadratic field ℚ(√D) is O(|D|55/112+ε) in general and O(|D| 5/12+ε) if |D| has a divisor of size |D|5/6. These bounds follow as results of nontrivial estimates for the number of solutions to the congruence xa,≡, yb modulo q in the ranges x ≤ X and y ≤ Y, where a,b are nonzero integers and q is a square-free positive integer. Furthermore, it is shown that the number of elliptic curves over ℚ with conductor N is O(N55/112+ε)in general and O(N5/12+ε) if N has a divisor of size N5/6. These results are the first improvements to the trivial bound O(|D| 1/2+ε) and the resulting bound O(N1/2+ε) for the 3-part and the number of elliptic curves, respectively. © 2005 London Mathematical Society.
Duke Scholars
Published In
Journal of the London Mathematical Society
DOI
Publication Date
2005
Volume
71
Issue
3
Start / End Page
579 / 598
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Pierce, L. B. (2005). The 3-part of class numbers of quadratic fields. Journal of the London Mathematical Society, 71(3), 579–598. https://doi.org/10.1112/S002461070500637X
Pierce, L. B. “The 3-part of class numbers of quadratic fields.” Journal of the London Mathematical Society 71, no. 3 (2005): 579–98. https://doi.org/10.1112/S002461070500637X.
Pierce LB. The 3-part of class numbers of quadratic fields. Journal of the London Mathematical Society. 2005;71(3):579–98.
Pierce, L. B. “The 3-part of class numbers of quadratic fields.” Journal of the London Mathematical Society, vol. 71, no. 3, 2005, pp. 579–98. Scival, doi:10.1112/S002461070500637X.
Pierce LB. The 3-part of class numbers of quadratic fields. Journal of the London Mathematical Society. 2005;71(3):579–598.
Published In
Journal of the London Mathematical Society
DOI
Publication Date
2005
Volume
71
Issue
3
Start / End Page
579 / 598
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics