Elliptic functions. Second edition. (English) Zbl 0615.14018

Lang, Serge

Graduate Texts in Mathematics, 112. New York etc.: Springer-Verlag. XI, 326 p.; DM 78.00 (1987).

This book is unchanged from the first edition (by Addison-Wesley Publishing Company, 1973; Zbl 0316.14001) except for the corrections of some misprints, and two items: 1. John Coates pointed out to me a mistake in chapter 21, dealing with the L-functions for an order. Hence I have eliminated the reference to orders at that point, and deal only with the absolute class group. - 2. I have renormalized the functions in chapter 19, following D. Kubert and the author [in Math. Ann. 218, 61-96; 175-189; 273-285 (1975; Zbl 0311.14005)]. Thus I use the Klein forms and Siegel functions as in that reference. Actually, the final formulation of Kronecker’s second limit formula comes out neater under this renormalization.

MSC:

14Hxx	Curves in algebraic geometry
14-02	Research exposition (monographs, survey articles) pertaining to algebraic geometry
11-02	Research exposition (monographs, survey articles) pertaining to number theory
11R58	Arithmetic theory of algebraic function fields
11F03	Modular and automorphic functions
14H05	Algebraic functions and function fields in algebraic geometry
11G15	Complex multiplication and moduli of abelian varieties
14K22	Complex multiplication and abelian varieties
12-02	Research exposition (monographs, survey articles) pertaining to field theory