A geometrical approach to the theory of Jacobi forms

Jürg Kramer

Compositio Mathematica (1991)

  • Volume: 79, Issue: 1, page 1-19
  • ISSN: 0010-437X

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Kramer, Jürg. "A geometrical approach to the theory of Jacobi forms." Compositio Mathematica 79.1 (1991): 1-19. <http://eudml.org/doc/90097>.

@article{Kramer1991,
author = {Kramer, Jürg},
journal = {Compositio Mathematica},
keywords = {theta series; Jacobi forms; elliptic modular surface; Kodaira-Vanishing- Theorem; Riemann-Roch-Theorem; explicit formula; dimension; space of Jacobi cusp forms},
language = {eng},
number = {1},
pages = {1-19},
publisher = {Kluwer Academic Publishers},
title = {A geometrical approach to the theory of Jacobi forms},
url = {http://eudml.org/doc/90097},
volume = {79},
year = {1991},
}

TY - JOUR
AU - Kramer, Jürg
TI - A geometrical approach to the theory of Jacobi forms
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 79
IS - 1
SP - 1
EP - 19
LA - eng
KW - theta series; Jacobi forms; elliptic modular surface; Kodaira-Vanishing- Theorem; Riemann-Roch-Theorem; explicit formula; dimension; space of Jacobi cusp forms
UR - http://eudml.org/doc/90097
ER -

References

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  1. [1] T.M. Apostol, Modular Functions and Dirichlet Series in Number Theory, Graduate Texts in Math. 41, Springer-Verlag, Berlin-Heidelberg -New York (1976). Zbl0332.10017MR422157
  2. [2] A. Ash, D. Mumford, M. Rapoport, Y. Tai, Smooth Compactification of Locally Symmetric Varieties, Brookline, Massachusetts. Zbl0334.14007
  3. [3] R. Berndt, Meromorphe Funktionen auf Mumford's Kompaktifizierung der universellen elliptischen Kurve N-ter Stufe, J. reine und angew. Math. 326 (1981), 95-103. Zbl0456.12009MR711467
  4. [4] M. Eichler, D. Zagier, On the theory of Jacobi forms, Progress in Math.55, Birkhäuser- Verlag, Boston- Basel-Stuttgart (1984). Zbl0554.10018MR781735
  5. [5] K. Kodaira, On compact analytic surfaces II, III, Ann. of Math.77 (1963), 563-626, 78 (1963), 1-40. Zbl0171.19601MR184257
  6. [6] J. Kramer, Jacobiformen und Thetareihen, Manuscripta Math.54 (1986), 279-322. Zbl0588.10024MR819403
  7. [7] D. Mumford, Abelian Varieties, Oxford University Press (1970). Zbl0223.14022MR282985
  8. [8] D. Mumford, Tata Lectures on Theta I, Progress in Math.28, Birkhäuser-Verlag, Boston- Basel-Stuttgart (1983). Zbl0509.14049MR688651
  9. [9] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, Vol. 24, No. 1 (1972), 20-59. Zbl0226.14013MR429918
  10. [10] N.-P. Skoruppa, The Dimensions of the Spaces of Jacobi Forms, Preprint (1989). 
  11. [11] N.-P. Skoruppa, D. Zagier, A trace formula for Jacobi Forms, J. reine und angew. Math. (to appear). Zbl0651.10019MR972365
  12. [12] Séminaire de Géométrie Algébrique du Bois-Marie 1965-66 SGA 5: Cohomologie 1-adique et Fonctions L, Lecture Notes in Math. 589, Springer-Verlag, Berlin-Heidelberg - New York (1977). Zbl0345.00011

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