Algebraic number theory. 2nd ed. (English) Zbl 0811.11001

Graduate Texts in Mathematics. 110. New York: Springer-Verlag. xiii, 357 p. (1994).
[The first ed. (1986) has been reviewed in Zbl 0601.12001.]
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.”
For this edition there are two new journal references: (a) J. Jorgenson and S. Lang, “A Parseval formula for functions with an asymptotic expansion at the origin”, Lect. Notes Math. 1564 (1993; Zbl 0788.30003); and (b) N.-P. Skoruppa, “Quick lower bounds for regulators of number fields”, Enseign. Math. 39, 137-141 (1993; Zbl 0803.11060).
There is a very interesting article of 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.


11-02 Research exposition (monographs, survey articles) pertaining to number theory
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11Rxx Algebraic number theory: global fields
11Sxx Algebraic number theory: local fields