Journal of the Mathematical Society of Japan

On Siegel-Eisenstein series attached to certain cohomological representations

Takuya MIYAZAKI

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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.

Article information

Source
J. Math. Soc. Japan, Volume 63, Number 2 (2011), 599-646.

Dates
First available in Project Euclid: 25 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1303737799

Digital Object Identifier
doi:10.2969/jmsj/06320599

Mathematical Reviews number (MathSciNet)
MR2793112

Zentralblatt MATH identifier
1276.11072

Subjects
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

Keywords
real analytic Eisenstein series cohomological representations confluent hypergeometric functions Dirichlet series

Citation

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


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