In mathematics, the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve. Peter Swinnerton-Dyer · Bryan John Birch · Hasse–Weil zeta function

This conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points.

The Birch and Swinnerton-Dyer conjecture is a conjecture on the relation between two important properties of an elliptic curve: an analytic part and an ...

22 окт. 2024 г. · In 2000 the Birch and Swinnerton-Dyer conjecture was designated a Millennium Problem, one of seven mathematical problems selected by the Clay ...

Conjecture (Birch and Swinnerton-Dyer). The Taylor expansion of L(C, s) at s = 1 has the form. L(C, s) = c(s − 1)r + higher order terms with c 6= 0 and r ...

4 авг. 2023 г. · The Birch and Swinnerton-Dyer conjecture is a conjecture about the form of the first non-vanishing derivative of the Hasse-Weil L-function of an ...

This is an introductory graduate-level textbook about the Birch and Swinnerton-. Dyer conjecture and modern approaches to the arithmetic of elliptic curves.

One of the seven Millennium Problems of the Clay Mathematics Institute in Cambridge,. Massachusetts is the Birch Swinnerton-Dyer conjecture, named after two ...

20 июн. 2022 г. · We give a complete proof of the conjecture of Birch and Swinnerton-Dyer for E/F, as well as its equivariant refinement formulated by Gross, ...

Citations in EuDML Documents · Nicole Arthaud, On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. · Serge Lang, Sur la ...