On the Birch and Swinnerton-Dyer conjecture for elliptic curves over totally real number fields (original) (raw)

This paper investigates the Birch and Swinnerton-Dyer conjecture for elliptic curves defined over totally real number fields. It establishes connections between the L-functions associated with these curves and their rank via the modularity of elliptic curves. Using key results from the theory of Mordell-Weil groups and long-established conjectures, the author provides both conjectural endpoints and proofs for specific cases, contributing to the understanding of how elliptic curves over these fields behave in relation to their modules.