# EXACT FORMULA FOR JACOBI-EISENSTEIN SERIES OF SQUARE FREE DISCRIMINANT LATTICE INDEX

• Xiong, Ran (School of Mathematical Sciences Tongji University)
• Accepted : 2019.08.23
• Published : 2020.03.31

#### Abstract

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

#### Acknowledgement

Supported by : Central Universities of China

#### References

1. A. Ajouz, Hecke operators on Jacobi forms of lattice index and the relation to elliptic modular forms, Ph.D. thesis, University of Siegen, 2015.
2. J. H. Bruinier and M. Bundschuh, On Borcherds products associated with lattices of prime discriminant, Ramanujan J. 7 (2003), no. 1-3, 49-61. https://doi.org/10.1023/A:1026222507219
3. J. H. Bruinier and M. Kuss, Eisenstein series attached to lattices and modular forms on orthogonal groups, Manuscripta Math. 106 (2001), no. 4, 443-459. https://doi.org/10.1007/s229-001-8027-1
4. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, third edition, Grundlehren der Mathematischen Wissenschaften, 290, Springer-Verlag, New York, 1999. https://doi.org/10.1007/978-1-4757-6568-7
5. M. Eichler and D. Zagier, The theory of Jacobi forms, Progress in Mathematics, 55, Birkhauser Boston, Inc., Boston, MA, 1985. https://doi.org/10.1007/978-1-4684-9162-3
6. A. Mocanu, Poincare and Eisenstein series for Jacobi forms of lattice index, arXiv1712.08174v2, 2018.
7. M. Woitalla, Calculating the Fourier coecients of Jacobi-Eisenstein series, arXiv1705.04595v2, 2017.