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Birch 1965 — Notes on elliptic curves. II
chain
B. J. Birch, H. P. F. Swinnerton-Dyer (1965). Notes on elliptic curves. II. J. reine angew. Math. 218 (1965) 79–108. DOI 10.1515/crll.1965.218.79. Canonical: https://doi.org/10.1515/crll.1965.218.79. Cited by its record. License as found: De Gruyter — publisher's copyright, cited. What it gave the chain: the conjecture: the rank is the order of vanishing of L(E, s) at s = 1, from EDSAC computations.
source
card id
card_chain_birch_swinnerton_dyer_1965
address
WIT.codex.FCT/notes-on-elliptic-curves-ii/REF.WITNESSED@b-j-birch-h-p-f-swinnert
adjoining cards
- builds on → Néron 1965 — Quasi-fonctions et hauteurs sur les variétés abéliennes — the conjecture: the rank is the order of vanishing of L(E, s) at s = 1, from EDSAC computa
- builds on → Weil 1949 — Numbers of solutions of equations in finite fields — the conjecture: the rank is the order of vanishing of L(E, s) at s = 1, from EDSAC computa
- enables → Coates 1977 — On the conjecture of Birch and Swinnerton-Dyer — for curves with complex multiplication, L(E, 1) != 0 forces rank zero - the first theorem
- enables → Gross 1986 — Heegner points and derivatives of L-series — L'(E, 1) is the height of a Heegner point: analytic rank one gives a point of infinite ord
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