The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k-Reference-Cited by-同舟云学术

The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k

Published:2019-08-12 Issue:1 Volume:101 Page:299-327
ISSN:0024-6107
Container-title:Journal of the London Mathematical Society
language:en
Short-container-title:J. London Math. Soc.

Author:

Bhargava Manjul¹,Elkies Noam²,Shnidman Ari³

Affiliation:

1. Department of Mathematics Princeton University Princeton NJ 08544 USA

2. Department of Mathematics Harvard University Cambridge MA 02138 USA

3. Einstein Institute of Mathematics Hebrew University of Jerusalem Edmund J. Safra Campus 9190401 Jerusalem Israel

Funder

National Science Foundation

Publisher

Wiley

Subject

General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1112/jlms.12271

Reference43 articles.

1. L.Alpoge ‘The average number of integral points on elliptic curves is bounded’ Preprint 2014 arXiv:1412.1047.

2. Higher composition laws I: A new view on Gauss composition, and quadratic generalizations

3. Mass formulae for local fields, and conjectures on the density of number fields discriminants;Bhargava M.;Int. Math. Res. Not.,2007

4. M.Bhargava Z.Klagsbrun R. L.OliverandA.Shnidman ‘Three‐isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field’ Preprint 2017 arXiv:1709.09790.

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Cube sum problem for integers having exactly two distinct prime factors;Proceedings - Mathematical Sciences;2023-11-30

2. The 3-Isogeny Selmer Groups of the Elliptic Curves y2=x3+n2;International Mathematics Research Notices;2023-11-23

3. Rank growth of elliptic curves over -th root extensions;Transactions of the American Mathematical Society, Series B;2023-04-14

4. Arithmetic statistics of Prym surfaces;Mathematische Annalen;2022-04-12

5. Elements of prime order in Tate–Shafarevich groups of abelian varieties over;Forum of Mathematics, Sigma;2022