Ranjan Roy

Elliptic and Modular Functions from Gauss to Dedekind to Hecke (eBook, PDF)

• Format: PDF

Produktbeschreibung

This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 18. April 2017
• Englisch
• ISBN-13: 9781108133784
• Artikelnr.: 48197914

Autorenporträt

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).

Inhaltsangabe

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.