Northcott property for special values of $L$-functions

3:00 pm, Wednesday, 1st May

Abstract

Pick an integer n. Consider a natural family of objects, such that each object $X$ in the family has an $L$-function $L(X,s)$. If we assume that the collection of special values $L(X,n)$ is bounded, does it imply that the family of objects is finite? We will first explain why we consider this question, in link with Kato's heights of mixed motives, and give two recent results: a Northcott property for families of Dedekind zeta functions, and a Northcott property for some families of $L$-functions attached to pure motives. This is joint work with Riccardo Pengo. The talk is aimed at mathematicians interested in number theory, and will contain several illustrating examples.