Author | Hirzebruch, Friedrich. author |
---|---|
Title | Manifolds and Modular Forms [electronic resource] / by Friedrich Hirzebruch, Thomas Berger, Rainer Jung |
Imprint | Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag, 1994 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-663-10726-2 |
Descript | XI, 212 p. online resource |
1 Background -- 2 Elliptic genera -- 3 A universal addition theorem for genera -- 4 Multiplicativity in fibre bundles -- 5 The Atiyah-Singer index theorem -- 6 Twisted operators and genera -- 7 Riemann-Roch and elliptic genera in the complex case -- 8 A divisibility theorem for elliptic genera -- Appendix I Modular forms -- 1 Fundamental concepts -- 2 Examples of modular forms -- 3 The Weierstraร ?-function as a Jacobi form -- 4 Some special functions and modular forms -- 5 Theta functions, divisors, and elliptic functions -- Appendix II The Dirac operator -- 1 The solution -- 2 The problem -- 1 Zolotarev polynomials -- 2 Interpretation as an algebraic curve -- 3 The differential equation โ revisited -- 4 Modular interpretation of Zolotarev polynomials -- 5 The embedding of the modular curve -- 6 Applications to elliptic genera -- Symbols