On Fourier-Jacobi expansions of real analytic Eisenstein series of degree 2

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Abstract

We discuss the Fourier-Jacobi expansion of certain vector valued Eisenstein series of degree 2, which is also real analytic. We show that its coefficients of index ±1 can be described by using a generating series of real analytic Jacobi forms. We also describe all the coefficients of general indices in suitable manners. Our method can be applied to study another Fourier series of Saito-Kurokawa type that is associated with a cusp form of one variable and half-integral weight. Then, following the arguments in the holomorphic case, we find that the Fourier series indeed defines a real analytic Siegel modular form of degree 2.

Original languageEnglish
Pages (from-to)85-122
Number of pages38
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume84
Issue number1
DOIs
Publication statusPublished - 2014

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Eisenstein Series
Jacobi
Fourier series
Jacobi Forms
Siegel Modular Forms
Cusp Form
Coefficient
Series

Keywords

  • Fourier-Jacobi expansion
  • Real analytic Eisenstein series
  • Skew-holomorphic Jacobi forms

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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AB - We discuss the Fourier-Jacobi expansion of certain vector valued Eisenstein series of degree 2, which is also real analytic. We show that its coefficients of index ±1 can be described by using a generating series of real analytic Jacobi forms. We also describe all the coefficients of general indices in suitable manners. Our method can be applied to study another Fourier series of Saito-Kurokawa type that is associated with a cusp form of one variable and half-integral weight. Then, following the arguments in the holomorphic case, we find that the Fourier series indeed defines a real analytic Siegel modular form of degree 2.

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