# 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.

4
questions

**57**

votes

**3**answers

6k 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 ...

**10**

votes

**5**answers

1k views

### 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 ...

**14**

votes

**3**answers

3k 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

**7**

votes

**2**answers

633 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/...