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Collected Papers III: 1978 - 1990

Serge Lang
Publication Date: 
Number of Pages: 
Springer Collected Works in Mathematics
[Reviewed by
Fernando Q. Gouvêa
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I have always been a fan of “collected works” volumes. Even in a time of easy electronic access to many journals, it can be hard to find a copy of a seminar paper or something that appeared in an obscure venue, so these volumes provide access to important papers. By bringing together all of a mathematician’s work, such books help identify dominant interests and themes. And, of course, they have an archival function, since paper, after all, is something we know will survive the centuries, hope as we must that all the material in electronic format will survive as well.

Serge Lang was, of course, famously prolific, and his collected papers (not “works”, as that would require many more volumes for the books) fill five volumes. Originally published in 2000, they have now been reprinted in paperback. (Curiously, these volumes are not available as e-books.)

This third volume covers the years, 1978–1990, which include the period of my graduate education, so that I remember reading many of them. Lang often visited Harvard when I was a graduate student there, so I attended several lectures and even a course or two that he taught. His enthusiasms of that period are all represented in this volume. Included here, for example, are the latter part of Lang’s series of papers on modular units with D. Kubert and the article in the Bulletin of the AMS that arose from Lang’s Colloquium Lectures of 1981. (That article is partly responsible for my interest in modular forms…) Also here is the important paper, written with N. Katz, on geometric class field theory. Later in the 1980s, we see Lang becoming interested in Vojta’s conjectures, hyperbolic manifolds, and Nevanlinna Theory, and several articles on these topics are in the book.

The fifth volume covers 1993–1999, during which Lang wrote several papers, many with Jay Jorgenson, having to do with regularized products and series and the heat kernel. Some of these papers were originally collected in two Springer Lecture Notes volumes, both of which are included here entire.

Anyone who is interested in number theory and allied fields will find much worth reading in these books.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.

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