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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.