Abstract
We introduce a Siegel-Eisenstein series of degree 2 which generates a cohomological representation of Saito-Kurokawa type at the real place. We study its Fourier expansion in detail, which is based on an investigation of the confluent hypergeometric functions with spherical harmonic polynomials. We will also consider certain Mellin transforms of the Eisenstein series, which are twisted by cuspidal Maass wave forms, and show their holomorphic continuations to the whole plane.
| Original language | English |
|---|---|
| Pages (from-to) | 599-646 |
| Number of pages | 48 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 63 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2011 |
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Keywords
- Cohomological representations
- Confluent hypergeometric functions
- Dirichlet series
- Real analytic eisenstein series
ASJC Scopus subject areas
- Mathematics(all)
Cite this
On Siegel-Eisenstein series attached to certain cohomological representations. / Miyazaki, Takuya.
In: Journal of the Mathematical Society of Japan, Vol. 63, No. 2, 2011, p. 599-646.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On Siegel-Eisenstein series attached to certain cohomological representations
AU - Miyazaki, Takuya
PY - 2011
Y1 - 2011
N2 - We introduce a Siegel-Eisenstein series of degree 2 which generates a cohomological representation of Saito-Kurokawa type at the real place. We study its Fourier expansion in detail, which is based on an investigation of the confluent hypergeometric functions with spherical harmonic polynomials. We will also consider certain Mellin transforms of the Eisenstein series, which are twisted by cuspidal Maass wave forms, and show their holomorphic continuations to the whole plane.
AB - We introduce a Siegel-Eisenstein series of degree 2 which generates a cohomological representation of Saito-Kurokawa type at the real place. We study its Fourier expansion in detail, which is based on an investigation of the confluent hypergeometric functions with spherical harmonic polynomials. We will also consider certain Mellin transforms of the Eisenstein series, which are twisted by cuspidal Maass wave forms, and show their holomorphic continuations to the whole plane.
KW - Cohomological representations
KW - Confluent hypergeometric functions
KW - Dirichlet series
KW - Real analytic eisenstein series
UR - http://www.scopus.com/inward/record.url?scp=80052410759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052410759&partnerID=8YFLogxK
U2 - 10.2969/jmsj/06320599
DO - 10.2969/jmsj/06320599
M3 - Article
AN - SCOPUS:80052410759
VL - 63
SP - 599
EP - 646
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 2
ER -