Elliptic Functions and Elliptic Curves [Paperback]

A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves.A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. The exposition is clear and logically carries themes from earlier through to later topics. this enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. The exposition is clear and logically carries themes from earlier through to later topics. this enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logically carries themes from earlier through to later topics. This enthusiastic work of scholarship is made complete with the inclusion of some interesting historical details and a very comprehensive bibliography.Preface; 1. Introductory; 2. Weierstrass functions; 3. Invariants and the modular function; 4. The Jacobi functions; 5. The Riemann surface and the integral of the first kind; 6. Quasi-elliptic functions and integrals of the second and third kinds; 7. The ternary elliptic functions; 8. Transformations and modular relations; 9. Trigonometric expansions; 10. The theta functions; 11. Elliptic curves; 12. The plan curbic; 13. Elliptic quartic curves; Historical note; Bibliography; Index.