Ranks of Elliptic Curves and Random Matrix Theory by J. B. Conrey (PDF)

Description

Random matrix theory is an area of mathematics first developed by physicists interested in the energy levels of atomic nuclei, but it can also be used to describe some exotic phenomena in the number theory of elliptic curves. This book illustrates this interplay of number theory and random matrices. It begins with an introduction to elliptic curves and the fundamentals of modeling by a family of random matrices, and moves on to highlight the latest research. There are expositions of current research on ranks of elliptic curves, statistical properties of families of elliptic curves and their associated L-functions and the emerging uses of random matrix theory in this field. Most of the material here had its origin in a Clay Mathematics Institute workshop on this topic at the Newton Institute in Cambridge and together these contributions provide a unique in-depth treatment of the subject.

User’s Reviews

Product description Review “…certainly the most useful single source for articles on [this subject]…” The American Statistician Book Description This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices. About the Author Brian Conrey is the Executive Director of the American Institute of Mathematics. He is also Professor of Mathematics at the University of Bristol.David Farmer is the Associate Director of the American Institute of Mathematics.Francesco Mezzadri is a Lecturer in the Department of Mathematics, University of Bristol.Nina Snaith is a Lecturer in the Department of Mathematics, University of Bristol. Read more

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