Abstract
Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by "Kudla lifting", i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q).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.
| Original language | English |
|---|---|
| Pages (from-to) | 591-615 |
| Number of pages | 25 |
| Journal | Mathematische Zeitschrift |
| Volume | 259 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2008 Jul 1 |
| Externally published | Yes |
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Keywords
- Eisenstein-Poincaré series
- Quaternionic discrete series representation
- Real symplectic group of signature (1+, q-)
- Theta lifting
- Weil representation
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Theta lifting from elliptic cusp forms to automorphic forms on Sp(1, q). / Narita, Hiroaki.
In: Mathematische Zeitschrift, Vol. 259, No. 3, 01.07.2008, p. 591-615.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Theta lifting from elliptic cusp forms to automorphic forms on Sp(1, q)
AU - Narita, Hiroaki
PY - 2008/7/1
Y1 - 2008/7/1
N2 - Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by "Kudla lifting", i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q).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AB - Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by "Kudla lifting", i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q).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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UR - http://www.scopus.com/inward/citedby.url?scp=42549093106&partnerID=8YFLogxK
U2 - 10.1007/s00209-007-0239-8
DO - 10.1007/s00209-007-0239-8
M3 - Article
VL - 259
SP - 591
EP - 615
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3
ER -