Low-lying Zeros of Quadratic Dirichlet L-Functions (15rit197)

The Banff International Research Station will host the "Low-lying zeros of quadratic Dirichlet L-functions." workshop in Banff from August 9 to August 16, 2015.

Prime numbers form the building blocks of the natural numbers. As such, in number theory our goal is to improve our understanding of their behavior. The most important unknown question in number theory is the Riemann Hypothesis, first conjectured by Bernhard Riemann in 1859. In simple terms this conjecture tells us that the distribution of prime numbers amongst the natural numbers is as nice as possible. The original statement was given for a function called the Riemann zeta function, but this conjecture has since been generalized for many other families of what are called L-functions.

In 1973, Hugh Montgomery noticed that certain statistics about the zeros of the Riemann zeta function bear a striking similarity to statistics coming from random matrices. In recent years, these similarities were seen to be present for other families of L-functions as well. On such statistic of interest is called the 1-level density. In this project, we study delicate properties of the 1-level density for the family of quadratic Dirichlet L-functions.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).