Seoyoung Kim

Various results related to a conjecture of Nagao

In 1965, Birch and Swinnerton-Dyer formulated a conjecture on the Mordell-Weil rank r of elliptic curves. Following their idea, in 1997, Nagao formulated a conjecture which predicts the rank of an elliptic curve over Q(T). In this talk, we relate the conjecture of Nagao to the conjecture of Birch and Swinnerton-Dyer, and further relate them to the Riemann hypothesis for elliptic curves. Furthermore, we discuss a generalization of the above results for the Selberg classes and hence (conjecturally) for larger classes of L-functions.