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Results tagged with birch-swinnerton-dyer
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user 1384
Questions related to the Birch and Swinnerton-Dyer conjecture about the vanishing order and first Taylor coefficient of the L-functions of elliptic curves at the point 1.
9
votes
What is the smallest positive integer for which the congruent number problem is unsolved?
Kazuo Matsuno writes (personal communication):
"I verified (10 years ago) by using mwrank and magma that E_N:y^2=x^3-N^2x
has a non-torsion point if N<=10^6 is congruent to 1,2,3 modulo 8 and
the ana …
- 41.4k
17
votes
2
answers
2k
views
What is the smallest positive integer for which the congruent number problem is unsolved?
The congruent number problem is the problem of figuring out whether a given positive integer $N$ is the area of a right-angled triangle with all side lengths rational. According to Dickson's "History …
- 41.4k
40
votes
Accepted
How did Birch and Swinnerton Dyer arrive at their conjecture?
For what it's worth, here are some historical comments.
Both Birch and S-D spoke in Cambridge a few weeks ago, on the history of their conjecture. To my surprise, both of them emphasized the role not …
- 41.4k