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Arithmetic Statistics |
| January 10, 2011 to May 20, 2011 |
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| Organized By: Brian Conrey (American Institute of Mathematics), John Cremona (University of Warwick), Barry Mazur (Harvard University), Michael Rubinstein* (University of Waterloo), Peter Sarnak (Princeton University), Nina Snaith (University of Bristol), and William Stein (University of Washington) |
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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. |
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Questions about this program should be sent either by email to the
Program Coordinator or by regular mail to:
Arithmetic Statistics
Mathematical Sciences Research Institute
17 Gauss Way, Berkeley, CA
94720-5070.
USA
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