Product formulas for modular forms on O ( 2 , n )

Maxim Kontsevich

Séminaire Bourbaki (1996-1997)

  • Volume: 39, page 41-56
  • ISSN: 0303-1179

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Kontsevich, Maxim. "Product formulas for modular forms on $O(2,n)$." Séminaire Bourbaki 39 (1996-1997): 41-56. <http://eudml.org/doc/110237>.

@article{Kontsevich1996-1997,
author = {Kontsevich, Maxim},
journal = {Séminaire Bourbaki},
keywords = {automorphic forms; Kac-Moody algebras; theta correspondence; theta functions; multiplicative correspondence; modular forms; meromorphic modular forms; K3 surfaces; mirror symmetry; string theory; Donaldson invariants},
language = {eng},
pages = {41-56},
publisher = {Société Mathématique de France},
title = {Product formulas for modular forms on $O(2,n)$},
url = {http://eudml.org/doc/110237},
volume = {39},
year = {1996-1997},
}

TY - JOUR
AU - Kontsevich, Maxim
TI - Product formulas for modular forms on $O(2,n)$
JO - Séminaire Bourbaki
PY - 1996-1997
PB - Société Mathématique de France
VL - 39
SP - 41
EP - 56
LA - eng
KW - automorphic forms; Kac-Moody algebras; theta correspondence; theta functions; multiplicative correspondence; modular forms; meromorphic modular forms; K3 surfaces; mirror symmetry; string theory; Donaldson invariants
UR - http://eudml.org/doc/110237
ER -

References

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  3. [3] R. Borcherds - Automorphic forms on Os+2,2 and infinite products, Invent. Math.120 (1995), 161-213. Zbl0932.11028MR1323986
  4. [4] R. Borcherds - The moduli space of Enriques surfaces and the fake monster Lie superalgebra, Topology35 no. 3 (1996), 699-710. Zbl0886.14015MR1396773
  5. [5] R. Borcherds - Automorphic forms with singularities on Grassmanians, e-print alg-geom/9609022 (1996). 
  6. [6] A. Borel, H. Jacquet - Automorphic forms and automorphic representations, Proc. Symp. Pure Math.33 part 1 (1979), 189-202. Zbl0414.22020MR546598
  7. [7] R. Dijkgraaf, G. Moore, E. Verlinde, H. Verlinde - Elliptic genera of symmetric products and second quantized strings, e-print hep-th/9608096 (1996). 
  8. [8] V. Gritsenko, V. Nikulin - Siegel automorphic form corrections of some Lorentzian Kac-Moody algebras , e-print alg-geom/9504006 (1995). 
  9. [9] V. Gritsenko, V. Nikulin - K3 surfaces, Lorentzian Kac-Moody algebras and Mirror Symmetry, Math. Res. Letters3 (1996), 211-229. Zbl0871.14031MR1386841
  10. [10] V. Gritsenko, V. Nikulin - The Igusa modular forms and "the simplest" Lorentzian Kac-Moody algebras, e-print alg-geom/9603010 (1996). Zbl0876.17026MR1438983
  11. [11] B. Gross, D. Zagier - On singular moduli, Jour. für die Reine und ang. Math.355 (1985), 191-220. Zbl0545.10015MR772491
  12. [12] J. Harvey, G. Moore - Algebras, BPS states and strings, e-print hep-th/9510182; Nucl. Phys. B463 (1996), 315. Zbl0912.53056MR1393643
  13. [13] J. Harvey, G. Moore - On the algebras of BPS states, e-print hep-th/9609017 
  14. [14] R. Howe - θ-series and invariant theory, Proc. Symp. Pure Math.33 part 1 (1979), 275-285. Zbl0423.22016
  15. [15] J. Jorgenson, A. Todorov - An analytic discriminant for polarized K3 surfaces, preprint (1994). 
  16. [16] S. Rallis - On a relation between SL2 cusp forms and automorphic forms on orthogonal groups, Proc. Symp. Pure Math.33 part 1 (1979), 297-314. Zbl0425.10034MR546604

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