TY - JOUR
T1 - Theta lifting from elliptic cusp forms to automorphic forms on Sp(1, q)
AU - Narita, Hiro Aki
N1 - Funding Information:
The author was partially supported by JSPS Research Fellowships for Young Scientist for April 2002 to March 2005. The results of this paper were obtained in this period.
PY - 2008/7
Y1 - 2008/7
N2 - Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by "Kudla lifting", i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q). We prove that the images of Arakawa's theta lifting belong to the space of bounded automorphic forms generating quaternionic discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincaré series generating such discrete series.
AB - Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by "Kudla lifting", i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q). We prove that the images of Arakawa's theta lifting belong to the space of bounded automorphic forms generating quaternionic discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincaré series generating such discrete series.
KW - Eisenstein-Poincaré series
KW - Quaternionic discrete series representation
KW - Real symplectic group of signature (1+, q-)
KW - Theta lifting
KW - Weil representation
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U2 - 10.1007/s00209-007-0239-8
DO - 10.1007/s00209-007-0239-8
M3 - Article
AN - SCOPUS:42549093106
SN - 0025-5874
VL - 259
SP - 591
EP - 615
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -