Numerical experiments with plectic Darmon points

Abstract: Let E/F be an elliptic curve defined over a number field F, and let K/F be a quadratic extension. If the analytic rank of E(K) is one, one can often use Heegner points (or the more general Darmon points) to produce (at least conjecturally) a nontorsion generator of E(K). If the analytic rank of E(K) is larger than one, the problem of constructing algebraic points is still very open. In recent work, Michele Fornea and Lennart Gehrmann have introduced certain p-adic quantities that may be conjecturally related to the existence of these points. In this talk I will explain their construction, and illustrate with some numerical experiments some support for their conjecture. This is joint work with Michele Fornea and Xevi Guitart.

number theory

Audience: researchers in the topic

( paper )

Algebra and Number Theory Seminars at Université Laval