https://link.springer.com/10.1007%2Fs11139-017-9986-2
We calculate the Jacobi Eisenstein series of weight k≥3 for a certain representation of the Jacobi group, and evaluate these at z=0 to give coefficient formulas for a family of modular forms Qk,m,β of weight k≥5/2 for the (dual) Weil representation on an even lattice. The forms we construct have rational coefficients and contain all cusp forms within their span. We explain how to compute the representation numbers in the coefficient formulas for Qk,m,β and the Eisenstein series of Bruinier and Kuss p-adically to get an efficient algorithm. The main application is in constructing automorphic products.
2018-12
en
https://scigraph.springernature.com/explorer/license/
research_article
2019-04-11T12:26
2018-12-01
true
articles
605-650
Poincaré square series for the Weil representation
Brandon
Williams
3a4314ed3eb0c960edcd0c16d21cea3ebcfa0dd3cc13ee96f32f7e15814ee60d
readcube_id
University of California, Berkeley
University of California, Berkeley, CA, USA
doi
10.1007/s11139-017-9986-2
Pure Mathematics
Mathematical Sciences
1382-4090
The Ramanujan Journal
1572-9303
dimensions_id
pub.1101631093
47
Springer Nature - SN SciGraph project
3