L functions

Type: Concept

As of November 2026, L functions has been mentioned in one podcast episode on Institute for Advanced Study (Dec 2025). Central mathematical concept discussed in the context of automorphic representations and their relationships to periods and special cycles.

An L-function is a meromorphic function on the complex plane, and one out of several categories of mathematical objects studied in analytic number theory and related fields. L-functions share fundamental properties and characteristics with the Riemann zeta function, which serves as the prototypical example of an L-function; therefore, L-functions are generalisations of the Riemann zeta function. Some important conjectures involving L-functions are, consequently, the Riemann hypothesis and its ge