Automorphic forms with singularities on Grassmannians

Inventiones Mathematicae

Volumn 132, Issue 3, 1998, Pages 491-562

  Borcherds, Richard E ^a  

^a DPMMS   (United Kingdom)

Author keywords

[No Author keywords available]

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EID: 0032377338     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050232     Document Type: Article

References (38)

1. P. Aspinwall, D. Morrison: String theory on K3 surfaces, in "Mirror symmetry II", 703-716 AMS/IP Stud. Adv. Math. 1, Amer. Math. Soc. 1997
2. W. Barth, C. Peters, A. Van de Ven, "Compact complex surfaces", Springer Verlag, 1984
3. R. E. Borcherds: Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109, 405-444(1992)
4. s+2.2(R) and infinite products, Invent. Math. 120, p. 161-213 (1995)
5. R. E. Borcherds: The moduli space of Enriques surfaces and the fake monster Lie superalgebra. Topology vol. 35 no. 3, 699-710, (1996)
6. A. Borel, W. Casselman: Automorphic forms, representations, and L-functions, Proc. Symp. Pure Math. Vol. XXXIII, A.M.S. (1979)
7. H. Cohen: Sums involving the values at negative integers of L-functions of quadratic characters. Math. Ann. 217, 271-285 (1975)
8. J. H. Conway: The automorphism group of the 26 dimensional even Lorentzian lattice. J. Algebra 80 (1983) 159-163. This paper is reprinted as chapter 27 of [C-S]
9. J. H. Conway, N. J. A. Sloane: Sphere packings, lattices and groups. Springer-Verlag New York 1988, Grundlehren der mathematischen Wissenschaften 290
10. S. Donaldson: Irrationality and the h-cobordism conjecture, J. Differential Geometry 26 141-168 (1987)
11. M. Eichler, D. Zagier: "The theory of Jacobi forms", Progress in mathematics vol. 55, Birkhäuser, Boston, Basel, Stuttgart 1985
12. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi: "Higher transcendental functions", vols. 1-3, and "Tables of integral transforms", vols 1-2, McGraw-Hill Book Company Inc, New York, Toronto, London 1953
13. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi: "Higher transcendental functions", vols. 1-3, and "Tables of integral transforms", vols 1-2, McGraw-Hill Book Company Inc, New York, Toronto, London 1953
14. I. Frenkel, A. Feingold: A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2, Math. Ann. 263 (1983) no. 1, 87-144
15. + = 1"
16. + = 1"
17. V. A. Gritsenko: Jacobi functions of n variables. J. Soviet Math. 53, 243-252 (1991) (The original Russian is in Zap. Nauch. Seminars of LOMI v. 168, p. 32-45 (1988))
18. V. A. Gritsenko: Jacobi functions of n variables. J. Soviet Math. 53, 243-252 (1991) (The original Russian is in Zap. Nauch. Seminars of LOMI v. 168, p. 32-45 (1988))
19. V. A. Gritsenko, V. V. Nikulin: Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras. Amer. J. Math. 119 (1997), no. 1, 181-224. Automorphic correction of a Lorentzian Kac-Moody algebra. C.R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 9, 1151-1156. Also see the preprints by these authors on the alg-geom preprint server http://xxx.lanl.gov/archive/alg-geom/
20. V. A. Gritsenko, V. V. Nikulin: Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras. Amer. J. Math. 119 (1997), no. 1, 181-224. Automorphic correction of a Lorentzian Kac-Moody algebra. C.R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 9, 1151-1156. Also see the preprints by these authors on the alg-geom preprint server http://xxx.lanl.gov/archive/alg-geom/
21. J. Harvey, G. Moore: Algebras, BPS states, and strings. Nuclear Phys. B 463 (1996), no. 2-3, 315-368. preprint hep-th/9510182
22. J. Harvey, G. Moore: Exact Gravitational Threshold Correction in the FHSV Model, preprint hep-th/9611176
23. D. Hejhal: Some observations concerning eigenvalues of the Laplacian and Dirichlet L-series, in H. Halberstam and C. Hooley (Eds.), ́Recent Progress in Analytic Number Theorý. Academic, London, 95-110 (1981)
24. D. Hejhal: The Selberg trace formula for PSL(2, R) Vol. 2. Springer Lecture notes in Mathematics vol. 1001, (1983)
25. J. Jorgenson, A. Todorov: Enriques surfaces and analytic discriminants, preprint (1995). An analytic discriminant for polarized K3 surfaces. (1994) preprint
26. J. Jorgenson, A. Todorov: Enriques surfaces and analytic discriminants, preprint (1995). An analytic discriminant for polarized K3 surfaces. (1994) preprint
27. 0(4), Math. Ann. 248, 249-266 (1980)
28. M. Kontsevich: Product formulas for modular forms on O(2, n). Séminaire Nicolas Bourbaki 821, November (1996)
29. W. Lerche, A. N. Schellekens, N. P. Warner: "Lattices and strings", Phys. Representation. 177, 1-140 (1989)
30. S. Niwa: Modular forms of half integral weight and the integral of certain theta functions, Nagoya Math J. 56, 147-163 (1975)
31. T. Oda: On modular forms associated with indefinite quadratic forms of signature (2, n - 2), Math. Ann. 231, 97-144 (1977)
32. 2 cusp forms and cusp forms on tube domains associated to orthogonal groups, Trans. AMS 263, 1-58 (1981)
33. U. Ray: A character formula for generalized Kac-Moody superalgebras, J. Algebra 177, no. 1, 154-163 (1995)
34. G. Shimura: On modular forms of half integral weight, Ann. of Math. (2) 97, 440-481 (1973)
35. T. Shintani: On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58, 83-126 (1975)
36. 19.1(Z), Soviet Math. 19, No 1 194-197 (1978)
37. A. Weil: Sur certains groupes d'opérateurs unitaires, Acta Math. 111, pp. 143-211
38. D. Zagier: Nombres de classes et formes modulaires de poids 3/2, C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 21, Ai, A883-A886