Number Theory Seminar

One approach to studying the p-adic behavior of L-functions relies on understanding p-adic properties of certain modular forms, for example congruences satisfied by their Fourier coefficients. In this talk, I will give an overview of p-adic L-functions and an approach to constructing them, which relies on relating them to certain p-adic families of Eisenstein series. I will start with the earliest examples of p-adic L-functions (due to Serre, Leopoldt, and Kubota) and conclude by mentioning a recently completed construction of myself, Harris, Li, and Skinner.