Questions tagged [birch-swinnerton-dyer]

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.

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63 votes
3 answers
7k views

Is there a "Basic Number Theory" for elliptic curves?

Tate's thesis showed how to profitably analyze $\zeta$ functions of number fields in terms of adelic points on the multiplicative group. In particular, combining Fourier analysis and topology, Tate ...
David E Speyer's user avatar
14 votes
3 answers
4k views

Recent progress toward Birch and Swinnerton-Dyer conjecture

Has there been any progress toward the Birch and Swinnerton-Dyer conjecture after The current status of the Birch & Swinnerton-Dyer Conjecture
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12 votes
5 answers
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Clarification on the weak BSD conjecture

It is usually told that Birch and Swinnerton-Dyer developped their famous conjecture after studying the growth of the function $$ f_E(x) = \prod_{p \le x}\frac{|E(\mathbb{F}_p)|}{p} $$ as $x$ tends to ...
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7 votes
2 answers
792 views

Power series expansions of $L$-series

Let $\zeta_K(s)$ be the Dedekind zeta function for a number field $K$. We can understand the first non-vanishing coefficient of its Laurent series via the class number formula. Is anything known/...
flor.ian sprung's user avatar