Abstract
Let p be a prime for which the congruence group Γ0(p)* is of genus zero, and j * p be the corresponding Hauptmodul. We investigate the twisted traces of singular values of j * p and construct infinite products related to them.
Similar content being viewed by others
References
Bringmann, K., Ono, K.: Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series. Math. Ann. 337, 591–612 (2007)
Bruinier, J.H., Funke, J.: Traces of CM-values of modular functions. J. Reine Angew. Math. 594, 1–33 (2006)
Bruinier, J.H., Ono, K.: Heegner divisors, L-functions and harmonic weak Maass forms (preprint)
Chen, I., Yui, N.: Singular values of Thompson series. In: Arasu, K.T., et al. (eds.) Groups, Difference Sets and Monster, pp. 255–326. de Gruyter, Berlin (1995)
Cohen, H.: Sums involving the values at negative integers of L-functions of quadratic characters. Math. Ann. 217, 271–285 (1975)
Conway, J.H., Norton, S.P.: Monstrous moonshine. Bull. Lond. Math. Soc. 11, 308–339 (1979)
Cox, D.: Primes of the Form x 2+ny 2. Wiley, New York (1989)
Eichler, M., Zagier, D.: The Theory of Jacobi Forms. Progress in Math., vol. 55. Bikhäuser, Boston (1985)
Gross, B., Kohnen, W., Zagier, D.: Heegner points and derivatives of L-series II. Math. Ann. 278, 497–562 (1987)
Kim, C.H.: Borcherds products associated with certain Thompson series. Compos. Math. 140, 541–551 (2004)
Kim, C.H.: Traces of singular values and Borcherds products. Bull. Lond. Math. Soc. 38, 730–740 (2006)
Koike, M.: On Replication Formula and Hecke Operators. Nagoya University (preprint)
Norton, S.P.: More on moonshine. In: Computational Group Theory, pp. 185–193. Academic, San Diego (1984)
Zagier, D.: Modular forms and differential operators. Proc. Indian Acad. Sci. 104, 57–75 (1994)
Zagier, D.: Traces of singular moduli. In: Motives, Polylogarithms and Hodge Theory, Part I (Irvine, CA, 1998). Int. Press Lect. Ser., vol. 3, I, pp. 211–244. Int. Press, Somerville (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-331-C00006).
Rights and permissions
About this article
Cite this article
Kim, C.H. Twisted traces of singular values. Ramanujan J 19, 237–246 (2009). https://doi.org/10.1007/s11139-007-9113-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11139-007-9113-x
Keywords
- Modular function
- Twisted trace
- Modular form
- Jacobi form
- Modular group
- Congruence subgroup
- Hauptmodul
- Singular values