Lang, Serge Elliptic functions. Second edition. (English) Zbl 0615.14018 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. Cited in 4 ReviewsCited in 114 Documents 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 PDF BibTeX XML OpenURL