Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 63, Number 2 (2011), 599-646.
On Siegel-Eisenstein series attached to certain cohomological representations
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.
J. Math. Soc. Japan, Volume 63, Number 2 (2011), 599-646.
First available in Project Euclid: 25 April 2011
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations 11F30: Fourier coefficients of automorphic forms
MIYAZAKI, Takuya. On Siegel-Eisenstein series attached to certain cohomological representations. J. Math. Soc. Japan 63 (2011), no. 2, 599--646. doi:10.2969/jmsj/06320599. https://projecteuclid.org/euclid.jmsj/1303737799