分野別セミナー

Central L-values of elliptic curves encode much arithmetic information about these curves. Via the correspondence with modular forms, work of Waldspurger, Gross, and others further relates these L-values to arithmetic quadratic forms and quaternion algebras. In the first part of the talk, we will explicate some of these connections to draw interesting consequences with the aid of concrete examples. In the second part of the talk, we will discuss some conjectural generalizations to higher rank.