MSRI - Arithmetic Statistics

Brian Conrey (American Institute of Mathematics), John Cremona (University of Warwick, United Kingdom), Barry Mazur (Harvard University), Michael Rubinstein* (University of Waterloo, Canada ), Peter Sarnak (Princeton University), Nina Snaith (University of Bristol, United Kingdom), and William Stein (University of Washington)

Tags: Scientific

L -functions attached to modular forms and/or to algebraic varieties and algebraic number fields are prominent in quite a wide range of number theoretic issues, and our recent growth of understanding of the analytic properties of L-functions has already lead to profound applications regarding among other things the statistics related to arithmetic problems. This program will emphasize statistical aspects of L-functions, modular forms, and associated arithmetic and algebraic objects from several different perspectives — theoretical, algorithmic, and experimental.

We will bring together experts on modular forms, analytic number theory, arithmetic and algebraic geometry, mathematical physics, and computational number theory to investigate several difficult problems in number theory from the point of view of understanding their limiting behaviour. Some of the specific problems we will consider include: the moments and value distribution of L-functions, statistics of the zeros of L -functions, the distribution of Fourier coefficients of automorphic forms, statistics of Maass forms, asymptotics of number fields, asymptotics of ranks of elliptic curves.

Workshops:

Connections for Women: Arithmetic Statistics
January 27, 2011 to January 28, 2011

Introductory Workshop: Arithmetic Statistics
January 31, 2011 to February 4, 2011

Arithmetic Statistics
April 11, 2011 to April 15, 2011

Workshop(s):

Jan 27, 2011 to Jan 28, 2011 : Connections for Women: Arithmetic Statistics
Jan 31, 2011 to Feb 4, 2011 : Introductory Workshop: Arithmetic Statistics
Apr 11, 2011 to Apr 15, 2011 : Arithmetic Statistics