Elliptic Functions

Elliptic functions parametrize elliptic curves and the intermingling of theanalytic and algebraicarithmetic theory has been at the center of mathematicssince th... » 

Elliptic functions parametrize elliptic curves and the intermingling of theanalytic and algebraicarithmetic theory has been at the center of mathematicssince the early part of the nineteenth century. The book is divided into fourparts. In the first Lang presents the general analytic theory starting fromscratch. Most of this can be read by a student with a basic knowledge ofcomplex analysis. The next part treats complex multiplication including adiscussion of Deurings theory of ladic and padic representations andelliptic curves with singular invariants. Part three covers curves with nonintegral invariants and applies the Tate parametrization to give Serresresults on division points. The last part covers theta functions and theKronecker Limit Formula. Also included is an appendix by Tate on algebraicformulas in arbitrary charactistic. TOCBContentsB General Theory. ComplexMultiplication Elliptic Curves with Singular Invariants. Elliptic Curves withNonintegral Invariants. Theta Functions and Kronecker limit Formula.Bibliography. Index. «