Borcherds products and Chern classes of Hirzebruch-Zagier divisors

Inventiones Mathematicae

Volumn 138, Issue 1, 1999, Pages 51-83

  Bruinier, Jan Hendrik ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033239070     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050341     Document Type: Article

References (21)

1. [AbSt] M. Abramowitz and I. Stegun, Pocketbook of Mathematical Functions, Verlag Harri Deutsch (1984)
2. [As] T. Asai, On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin's convolution, J. Math. Soc. Jpn. 28 (1976), 48-61
3. s+2,2(ℝ) and infinite products, Invent. Math. 120 (1995), 161-213
4. [Bo2] R. E. Borcherds, Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998), 491-562
5. [Bo3] R. E. Borcherds, The Gross-Kohnen-Zagier theorem in higher dimensions, Duke Math. J. 97 (1999), 219-233
6. [Br] S. Breulmann, Estimates for Fourier coefficients of Siegel cusp forms of degree three, Math. Ann. 310 (1998), 129-160
7. [Bru] J. H. Bruinier, Borcherdsprodukte und Chernsche Klassen von Hirzebruch-Zagier-Zykeln, Dissertation, Universität Heidelberg (1998)
8. [DI] F. Diamond and J. Im, Modular forms and modular curves, Can. Math. Soc. Conf. Proc. 17 (1995), 39-133
9. [DN] K. Doi and H. Naganuma, On the functional equation of certain Dirichlet series, Invent. Math. 9 (1969), 1-14
10. [EMOT] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, McGraw-Hill (1954)
11. [Ge] G. van der Geer, Hilbert Modular Surfaces, Springer Verlag (1988)
12. [GR] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall (1965)
13. 2(script O sign), Lie groups and their representations. In: Proc. of the Summer School on Group Representations, I. M. Gelfand ed., A. Hilger (1975), 139-150
14. [He] D. A. Hejhal, The Selberg Trace Formula for PSL(2, ℝ), Lect. Notes Math. 1001, Springer-Verlag (1983)
15. [HZ] F. Hirzebruch und D. Zagier, Intersection Numbers of Curves on Hilbert Modular Surfaces and Modular Forms of Nebentypus, Invent. Math. 36 (1976), 57-113
16. [Na] H. Naganuma, On the coincidence of two Dirichlet series associated with cusp forms of Hecke's "Neben"-type and Hilbert modular forms over a real quadratic field, J. Math. Soc. Jpn. 25 (1973), 547-555
17. [Ni] D. Niebur, A class of nonanalytic automorphic functions, Nagoya Math. J. 52 (1973), 133-145
18. [Od] T. Oda, On Modular Forms Associated with Indefinite Quadratic Forms of Signature (2, n - 2), Math. Ann. 231 (1977) 97-144
19. [Sc] B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag (1974)
20. [Za1] D. Zagier, Modular Forms Associated to Real Quadratic Fields, Invent. Math. 30 (1975), 1-46
21. [Za2] D. Zagier, Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields. In: Modular Functions of One Variable VI, Lect. Notes Math. 627, Springer-Verlag (1977), 105-169