TY - JOUR
T1 - A converse theorem for Jacobi–Maass forms and applications
AU - Herrero-Miranda, Sebastián
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - We provide a converse theorem for Jacobi–Maass forms, as introduced by Pitale (2009), and give three applications. Firstly, we generalize a converse theorem for holomorphic Jacobi cusp forms due to Martin (1996) to non-cuspidal Jacobi forms. Secondly, we prove the analogue result for skew-holomorphic Jacobi forms, and thirdly, we give a new proof for the existence of an explicit isomorphism between half integral weight Maass forms in Kohnen's plus space of level 4 and Jacobi–Maass forms of index 1, first proved by Pitale (2009).
AB - We provide a converse theorem for Jacobi–Maass forms, as introduced by Pitale (2009), and give three applications. Firstly, we generalize a converse theorem for holomorphic Jacobi cusp forms due to Martin (1996) to non-cuspidal Jacobi forms. Secondly, we prove the analogue result for skew-holomorphic Jacobi forms, and thirdly, we give a new proof for the existence of an explicit isomorphism between half integral weight Maass forms in Kohnen's plus space of level 4 and Jacobi–Maass forms of index 1, first proved by Pitale (2009).
KW - Converse theorem
KW - Dirichlet series
KW - Functional equation
KW - Jacobi–Maass forms
UR - http://www.scopus.com/inward/record.url?scp=84978300243&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2016.05.005
DO - 10.1016/j.jnt.2016.05.005
M3 - Article
AN - SCOPUS:84978300243
SN - 0022-314X
VL - 169
SP - 41
EP - 61
JO - Journal of Number Theory
JF - Journal of Number Theory
ER -