On Siegel-Eisenstein series attached to certain cohomological representations

Takuya Miyazaki

doi:10.2969/jmsj/06320599

On Siegel-Eisenstein series attached to certain cohomological representations

Takuya Miyazaki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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	https://doi.org/10.2969/jmsj/06320599
Publication status	Published - 2011

Keywords

Cohomological representations
Confluent hypergeometric functions
Dirichlet series
Real analytic eisenstein series

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06320599

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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.",

keywords = "Cohomological representations, Confluent hypergeometric functions, Dirichlet series, Real analytic eisenstein series",

author = "Takuya Miyazaki",

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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

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JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -

On Siegel-Eisenstein series attached to certain cohomological representations

Abstract

Keywords

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