Takashi TAKEBE is a professor at the Faculty of Mathematics, National Research University Higher School of Economics, Moscow. He studies integrable systems in mathematical physics, especially integrable nonlinear differential equations, their connection with complex analysis and solvable lattice models in statistical mechanics related to elliptic R-matrices.
Introduction.
Chapter 1. The arc length of curves.
Chapter 2. Classification of elliptic integrals.
Chapter 3. Applications of elliptic integrals.
Chapter 4. Jacobi's elliptic functions on R.
Chapter 5. Applications of Jacobi's elliptic functions.
Riemann surfaces of algebraic functions.
Chapter 7. Elliptic curves.
Chapter 8. Complex elliptic integrals.
Chapter 9. Mapping the upper half plane to a rectangle.
Chapter 10. The Abel
Jacobi theorem.
Chapter 11. The general theory of elliptic functions.
Chapter 12. The Weierstrass ¿
function.
Chapter 13. Addition theorems.
Chapter 14. Characterisation by addition formulae.
Chapter 15. Theta functions.
Chapter 16. Infinite product factorisation of theta functions.
Chapter 17. Complex Jacobian functions.
Appendix A. Theorems in analysis and complex analysis.
Bibliography.
Index.
Introduction.- Chapter 1. The arc length of curves.- Chapter 2. Classification of elliptic integrals.- Chapter 3. Applications of elliptic integrals.- Chapter 4. Jacobi's elliptic functions on R.- Chapter 5. Applications of Jacobi's elliptic functions.- Riemann surfaces of algebraic functions.- Chapter 7. Elliptic curves.- Chapter 8. Complex elliptic integrals.- Chapter 9. Mapping the upper half plane to a rectangle.- Chapter 10. The Abel-Jacobi theorem.- Chapter 11. The general theory of elliptic functions.- Chapter 12. The Weierstrass -function.- Chapter 13. Addition theorems.- Chapter 14. Characterisation by addition formulae.- Chapter 15. Theta functions.- Chapter 16. Infinite product factorisation of theta functions.- Chapter 17. Complex Jacobian functions.- Appendix A. Theorems in analysis and complex analysis.- Bibliography.- Index.
