Ellen Eischen, University of Oregon, L-functions, modular forms, and congruences

Title: L-functions, modular forms, and congruences

Abstract: L-functions and modular forms are certain functions that play central roles in number theory. Starting with work of Euler and ending with my own recent work, I will introduce several key developments concerning relationships between the values of these functions. Along the way, I will highlight some striking congruences, which have implications for problems that a priori appear to have little to do with these congruences.