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. The purpose of this book is to
illustrate this interplay of number theory and random matrices. It
begins with an introduction to elliptic curves and the fundamentals
of modelling 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.
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