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 Sep 9 |
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Keywords
- Cohomological representations
- Confluent hypergeometric functions
- Dirichlet series
- Real analytic eisenstein series
ASJC Scopus subject areas
- Mathematics(all)