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Zbl 0811.11001
Lang, Serge
Algebraic number theory. 2nd ed. (English)
[B] Graduate Texts in Mathematics. 110. New York: Springer-Verlag. xiii, 357 p. DM 68.00; öS 530.40; sFr. 68.00 (1994). ISBN 0-387-94225-4/hbk

[The first ed. (1986) has been reviewed in Zbl 0601.12001.]\par Here are the first two sentences of the ``Preface for the 2nd edition'': ``The principal change in this new edition is a complete rewriting of Chapter XVII on the explicit formulas. Otherwise, I have made a few editions, and a number of corrections.''\par For this edition there are two new journal references: (a) {\it J. Jorgenson} and {\it S. Lang}, ``A Parseval formula for functions with an asymptotic expansion at the origin'', Lect. Notes Math. 1564 (1993; Zbl 0788.30003); and (b) {\it N.-P. Skoruppa}, ``Quick lower bounds for regulators of number fields'', Enseign. Math. 39, 137-141 (1993; Zbl 0803.11060).\par There is a very interesting article of {\it S. Lang} [``Mordell's review, Siegel's letter to Mordell's diophantine geometry, and 20th century mathematics'', Notices Am. Math. Soc. 42, No. 3, 339-350 (1995)]. It reproduces (and discusses extensively) a letter, highly critical, of Siegel in which this book is mentioned -- quite derisively. The article makes a fine case for the approach of this volume.
[M.Sheingorn (New York)]

MSC 2000:: *11-02 Research monographs (number theory)
11-01 Textbooks (number theory)
11Rxx Algebraic number theory: global fields
11Sxx Algebraic number theory: local and p-adic fields

Keywords: basic algebraic number theory; class field theory; analytic algebraic number theory; Brauer-Siegel theorem; zeta-functions; Tate thesis; $L$- series; ideles; adeles

Citations: Zbl 0601.12001; Zbl 0788.30003; Zbl 0803.11060

Cited in: Zbl 1165.11001

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