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Formal Fourier Jacobi expansions and special cycles of codimension two

Part of: Computational number theory Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  06 August 2015

Martin Westerholt-Raum
Martin Westerholt-Raum*
Affiliation:
Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111, Bonn, Germany email [email protected]
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Abstract

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We prove that formal Fourier Jacobi expansions of degree two are Siegel modular forms. As a corollary, we deduce modularity of the generating function of special cycles of codimension two, which were defined by Kudla. A second application is the proof of termination of an algorithm to compute Fourier expansions of arbitrary Siegel modular forms of degree two. Combining both results enables us to determine relations of special cycles in the second Chow group.

Keywords

special cycles of codimension twoformal Fourier Jacobi expansionscomputing Siegel modular forms

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F30: Fourier coefficients of automorphic forms 11Y40: Algebraic number theory computations
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 12 , December 2015 , pp. 2187 - 2211
Copyright
© The Author 2015 

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