Reciprocity Laws

Reciprocity Laws. From Euler to Eisenstein

has just appeared in Springer-Verlag Heidelberg. It is an updated version of Chapters 1 - 11 as they were available on this page for some time: here's the actual table of contents with ps and pdf file of Chapter 11 (corrected version), and I also have prepared a description of the content with a few examples. A table of errata is available as a tex file, as a dvi file, as a ps file, as a pdf file, and in html.

Here are some reviews of the book by F. Gouvea for MAA online, H. Opolka for Zentralblatt, Charles Helou for MathSciNet, D.V. Feldman for Choice Reviews online, Roland Auer, Ch. Baxa, N. Schappacher for the Semesterberichte, P. Shiu for the Math. Gazette, and S. Raghavan for Ganita-Bharati, a Bulletin of the Indian Society for History of Mathematics.

The combined bibliography can be found online, complete with references to the Mathematical Reviews, the Zentralblatt and the Jahrbuch. Moreover, I have a list of published proofs of the Quadratic Reciprocity Law. If your browser supports frames, I suggest you try the framed version. Here's a draft for a similar list of proofs of the Quartic Reciprocity Law.
Michael Berg has published a book on The Fourier-Analytic Proof of Quadratic Reciprocity at Wiley.
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Last update: July 12, 2001