This book is an introduction to the theory of elliptic curves, ranging from its elementary aspects to current research. This new edition contains three new chapters which explore recent directions and extensions of the theory and two new appendices: the first, by Stefan Theisan, examines the role of Calabi-Yau manifolds in string theory while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory.The 6-twist 105 : [K aagt; F2a#39; and the oo-twist woo : IK aagt; F5a#39;; are defined by the relations ... The twists satisfy 1b5(K*) : 1 and woo (K *) : 1, and thus they can be defined on the group C K : I 14/ K * of idele classes. ... Let zb be an algebraic Hecke character I K aagt; F *, and let go : F aagt; C be a complex embedding of F. Then the twist ... 1 1- X (pv)(Npv)as Again, rrv is a local uniformizing element in ( DU.
|Publisher||:||Springer Science & Business Media - 2004|