Washington State University
Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar
Department of Mathematics and Statistics
Neill Hall 5W
March 26, Monday, 4:10 - 5:00 PM
Matthew Jobrack
Department of Mathematics and Statistics
Washington State University
Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar
Department of Mathematics and Statistics
Neill Hall 5W
March 26, Monday, 4:10 - 5:00 PM
Matthew Jobrack
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.
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.