Elliptic and Modular Functions from Gauss to Dedekind to Hecke

Klappentext Many mathematicians today believe mathematical works from past centuries are inaccessible, not useful, or both. This book demonstrates that past works are not only readable, but brimming with ideas and insights. It is aimed at graduate students or researchers working in modular functions, number theory, complex analysis, or special functions.Many mathematicians today believe mathematical works from past centuries are inaccessible, not useful, or both. This book demonstrates that past works are not only readable, but brimming with ideas and insights. It is aimed at graduate students or researchers working in modular functions, number theory, complex analysis, or special functions.

Autorentext

Ranjan Roy is the Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers in differential equations, fluid mechanics, complex analysis, and the development of mathematics. He received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He is a co-author of three chapters in the NIST Handbook of Mathematical Functions, of Special Functions (with Andrews and Askey, Cambridge, 2010), and the author of Sources in the Development of Mathematics (Cambridge, 2011).

Klappentext

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

Inhalt

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.