On a BSD-type formula for L-values of Artin twists of elliptic curves

Abstract: In this talk we discuss the possible existence of a BSD-type formula for $L$-functions of elliptic curves twisted by Artin representations. After outlining some expected properties of these $L$-functions, we present arithmetic consequences for the behaviour of Tate–Shafarevich groups, Selmer groups and rational points. We illustrate these with some explicit examples. This is joint work with Vladimir Dokchitser and Robert Evans.

algebraic geometrynumber theory

Audience: researchers in the topic

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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