Elliptic and Modular Functions from Gauss to Dedekind to Hecke

ISBN-13: 9781107159389 / Angielski / Twarda / 2017 / 488 str.

Ranjan Roy

Opis

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

Recenzje

'This book will be a valuable resource for understanding modular functions in their historical context, especially for readers not fluent in the languages of the original papers.' Paul M. Jenkins, Mathematical Reviews

Spis treści

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.