The 1-2-3 of Modular Forms: Lectures at a Summer School in Nordfjordeid, NorwaySpringer Science & Business Media, 10 de febr. 2008 - 266 pàgines This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications. |
Continguts
| 1 | |
Eisenstein Series and the Discriminant Function | 12 |
Theta Series | 24 |
Hecke Eigenforms and Lseries | 37 |
Modular Forms and Differential Operators | 48 |
References and Further Reading | 99 |
Hilbert Modular Surfaces | 106 |
The Example Q 5 | 123 |
The Satake Isomorphism | 215 |
Relations in the Hecke Algebra | 218 |
Satake Parameters | 219 |
Lfunctions | 220 |
Liftings | 221 |
The Moduli Space of Principally Polarized Abelian Varieties | 226 |
Counting Points on Curves of Genus 2 | 230 |
The Ring of VectorValued Siegel Modular Forms for Genus 2 | 232 |
The Orthogonal Group O2n | 127 |
Additive and Multiplicative Liftings | 146 |
References | 176 |
The Siegel Modular Group | 183 |
The Fourier Expansion of a Modular Form | 189 |
Theta Series | 195 |
Moduli of Principally Polarized Complex Abelian Varieties | 201 |
Compactifications | 204 |
Roots and Representations | 207 |
Vector Bundles Defined by Representations | 209 |
Holomorphic Differential Forms | 210 |
Cusp Forms and Geometry | 212 |
The Classical Hecke Algebra | 213 |
Harders Conjecture | 235 |
Evidence for Harders Conjecture | 237 |
| 241 | |
A Congruence Between a Siegel and an Elliptic Modular Form Günter Harder 247 | 246 |
The Hecke Algebra and a Congruence | 250 |
The Special Values of the Lfunction | 252 |
Cohomology with Coefficients | 253 |
Why the Denominator? | 257 |
Arithmetic Implications | 258 |
References | 259 |
Appendix | 260 |
| 263 | |
Altres edicions - Mostra-ho tot
The 1-2-3 of Modular Forms: Lectures at a Summer School in Nordfjordeid, Norway Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier Previsualització no disponible - 2009 |
Frases i termes més freqüents
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