Department of Mathematics and Statistics
Washington State University
Title: L-Functions Associated to Modular Forms and the Non-Vanishing of their Derivatives at the Central Point
Abstract: Arithmetic objects
over the rationals, such as number fields or elliptic curves, often
have an associated complex-valued function called an L-function.
These functions can be studied analytically to derive useful
information about the object. In this talk I will introduce
L-functions, and give examples of different types as well as how they
are used. Then we will concentrate on families of L-functions
associated to modular forms, and an outline of the proof that a
positive proportion of these functions are non-vanishing at the central
point of s=1/2.