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

On Fourier–Jacobi expansions of real analytic Eisenstein series of degree 2 We discuss the Fourier–Jacobi expansion of certain vector valued Eisenstein series of degree $$2$$ 2 , which is also real analytic. We show that its coefficients of index $$\pm 1$$ ± 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

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

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References (25)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Algebra; Differential Geometry; Combinatorics; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-014-0092-8
Publisher site
See Article on Publisher Site

Abstract

We discuss the Fourier–Jacobi expansion of certain vector valued Eisenstein series of degree $$2$$ 2 , which is also real analytic. We show that its coefficients of index $$\pm 1$$ ± 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.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Apr 8, 2014

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