[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b190342

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

Xiong, Ran (School of Mathematical Sciences Tongji University)

Publication Information

Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 481-488 More about this Journal

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.

Keywords

Jacobi forms of lattice index; Fourier coefficients of Jacobi-Eisenstein series;

Citations & Related Records

Reference

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 DOI
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 DOI
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.