Elliptic and modular functions : from Gauss to Dedekind to Hecke / Ranjan Roy.

Includes bibliographical references and index.

1. The basic modular forms;
2. Gauss's contributions to modular forms;
3. Abel and Jacobi on elliptic functions;
4. Eisenstein and Hurwitz;
5. Hermite's transformation of theta functions;
6. Complex variables and elliptic functions;
7. Hypergeometric functions;
8. Dedekind's paper on modular functions;
9. The n function and Dedekind sums;
10. Modular forms and invariant theory;
11. The modular and multiplier equations;
12. The theory of modular forms as reworked by Hurwitz;
13. Ramanujan's Euler products and modular forms;
14. Dirichlet series and modular forms;
15. Sums of squares;
16. The Hecke operators;
Appendix.

A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.