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Surveys in Number Theory: Papers from The Millennial Conference on Number Theory

M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, and W. Philipp, editors
A K Peters
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
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This is an interesting idea. Conference proceedings sometimes contain a heterogeneous mix of articles that make it hard to justify purchasing a copy. At best, one will be interested in one or two papers. Surveys in Number Theory solves that problem by being selective. Instead of containing the full proceedings of the Millennial Conference on Number Theory (these were published separately in three large hardcover volumes called Number Theory for the Millennium), this book collects only those papers that might be of interest to a wider range of readers. For the most part, these are papers that survey recent work in various parts of number theory; most number theorists will find something to like here. And since the resulting book is shorter and in paperback, its price is very reasonable.

There are several very nice things in the book. Some of the topics covered are the Riemann Hypothesis, normal numbers, automorphic forms, Iwasawa theory, diophantine approximation, and Waring's Problem. Bjorn Poonen's article on how to compute rational points on curves is particularly good. There is an interesting essay by Robert A. Rankin on "G. H. Hardy As I Knew Him" that is likely to be of interest to historians of mathematics.

Given the size of the Millennial Conference, I think the idea of going for a two-tiered approach to publishing the conference proceedings was a good one. Large research libraries will very likely want to get the full three-volume set. Everyone else will probably be happy with this shorter version.

Fernando Q. Gouvêa ( is the author of several books, including, most recently, Math through the Ages, written in collaboration with William Berlinghoff.

The table of contents is not available.