Number Theory Seminar

Speaker: Asbjørn Nordentoft (Paris)

Title: Non-vanishing of finite order twists of L-functions via horizontal p-adic L-functions

Abstract:  Goldfeld’s Conjecture predicts that exactly 50% of quadratic twists of a fixed elliptic curve will have L-function vanishing at the central point. Similarly when considering the non-vanishing of higher order twists of elliptic curves, it has been predicted by David-Fearnly-Kisilevsky that a 100% should be non-vanishing. Very little is known beyond the quadratic case as the problem lies beyond the current technology of analytic number theory. In this talk I will present an algebraic approach relying on the p-adic interpolation of certain twisted moments of L-functions using a ‘horizontal p-adic L-function’ . I will also present applications to simultaneous non-vanishing. This is joint work in preparation with Daniel Kriz.