Reciprocity Laws
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.
I'm working on completing part II dealing with the development
from Kummer to Hilbert (the story from Takagi to Artin being
reserved for part III), but don't expect a preliminary draft before
2002. The planned content looks like
this.
The combined bibliography of vol I, II and III 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 just (Feb 2000) published a book on
The Fourier-Analytic Proof of Quadratic Reciprocity
at Wiley.
Webliography on Reciprocity Laws
- Quadratic
Reciprocity by Kevin Brown
- Gauß, Eisenstein, and the ``third'' proof of the
Quadratic Reciprocity Law by Reinhard C. Laubenbacher and
David J. Pengelley
- Eisenstein's Misunderstood Geometric Proof of the
Quadratic Reciprocity Law by Reinhard C. Laubenbacher and
David J. Pengelley
-
Quadratic Reciprocity Law by Donald Hazlewood and Carol Hazlewood
- A Trigonometric Proof of the
Quadratic Reciprocity Law by David R. Hayes and Joshua Holden
- The Jewel
of Arithmetic by Kevin Brown
-
Quadratic Reciprocity Law by Rama Kumandur
- Lois
de réciprocité quadratique by C. Banderier
-
Quadratic reciprocity in global fields by Paul Garrett
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Last update: July 12, 2001
