Reflection Groups of Lorentzian Lattices
نویسنده
چکیده
0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 1. Notation and terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 2. Modular forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 3. Discriminant forms and the Weil representation . . . . . . . . . . . . . . . . . . . . . . . . . 323 4. The singular theta correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 5. Theta functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 6. Eta quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 7. Dimensions of spaces of modular forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 8. The geometry of 0(N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 9. An application of Serre duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 10. Eisenstein series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 11. Reflective forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 12. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 13. Open problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
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Lattices like the Leech lattice
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