In the 1960s, Adams computed a large family of elements in the stable homotopy groups of spheres. The orders of those elements are closely related to special values of the Riemann zeta function. This hints at very deep connections between homotopy theory and L-functions.
In this talk, I will first review known connections between the two sides through the J-homomorphism and algebraic K-theory. Then I will discuss my recent and ongoing works in generalizing those connections to Dirichlet and Artin L-functions. Some of the results are joint work in progress with Elden Elmanto.