### Various results related to a conjecture of Nagao

Heilbronn Number Theory Seminar

31st May 2023, 4:00 pm – 5:00 pm

Fry Building, 2.04

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.

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