On Siegel-Eisenstein series attached to certain cohomological representations

Research output: Contribution to journalArticle

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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.

Original languageEnglish
Pages (from-to)599-646
Number of pages48
JournalJournal of the Mathematical Society of Japan
Volume63
Issue number2
DOIs
Publication statusPublished - 2011

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Eisenstein Series
Harmonic Polynomials
Confluent Hypergeometric Function
Mellin Transform
Fourier Expansion
Spherical Harmonics
Waveform
Continuation

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 journalArticle

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