Mathematics Colloquium: L-Functions and Modular Forms
4:10pm Neill 5W
L-functions are complex-analytic invariants attached to certain arithmetic or geometric objects. Since Riemanns investigation of the zeta function, the zeros of L-functions have been known to be closely related to many problems in number theory. In this talk, we will first give an overview of the philosophy and construction of L-functions, as well as some of their applications. Then we will look specifically at L-functions attached to classical modular forms, and some recent results concerning the non-vanishing of these functions at the central point.