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3 votes
0 answers
171 views

Rank and Taylor coefficient in Birch and Swinnerton–Dyer

I am trying to get a better understanding of the Birch and Swinnerton–Dyer conjecture. I have two questions Why might one expect that the analytic rank of $L(E,s)$ is equal to the rank of $E(\mathbb{...
Rdrr's user avatar
  • 901
17 votes
2 answers
3k views

Consequences of the Birch and Swinnerton-Dyer Conjecture?

Before asking my short question I had made some research. Unfortunately I did not find a good reference with some examples. My question is the following What are the consequences of the Birch and ...
14 votes
3 answers
2k views

Deducing BSD from Gross-Zagier and Kolyvagin

Does anyone know which papers deduce BSD for elliptic curves $E/\mathbb{Q}$ of rank 0 or 1 from the papers by Gross and Zagier and Kolyvagin? If I understand these theories right, there is still a ...
Amathena's user avatar
  • 993