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Restrictions of Jacobi Forms of Several Variables

With Special Emphasis on Quaternionic Jacobi Forms
  • Till DieckmannEmail author
Conference paper
  • 631 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 115)

Abstract

In this article we consider pullbacks from Jacobi forms with respect to a lattice L to lattices L 0 given by an isometric embedding \(\iota: L_{0} \rightarrow L\). We consider the special cases L = D 4 and \(L_{0} = L_{t} = (\mathbb{Z},tx^{2})\). In this case we can show that the pullback is an embedding and we study the dependency on the choice of ι. Combining this with earlier results of Krieg, we can define a family of index-raising operators J k, 1 → J k, t for all t, which interpolate the operators \(U_{l}: J_{k,1} \rightarrow J_{k,l^{2}}\) defined by Eichler and Zagier.

Keywords

Jacobi Forms Isometric Embedding Pullback Zagier Hurwitz Quaternions 
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Notes

Acknowledgement

We would like to thank the organizers for the nice conference and the referee for valuable suggestions.

References

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    M. Eichler, D. Zagier, The Theory of Jacobi Forms (Birkhäuser, Boston, 1985)CrossRefzbMATHGoogle Scholar
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    V.A. Gritsenko, Fourier-Jacobi functions of n. J. Sov. Math. 53, 243–252 (1991)Google Scholar
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    A. Hurwitz, Vorlesungen über die Zahlentheorie der Quaternionen (Springer, Berlin, 1919)CrossRefzbMATHGoogle Scholar
  4. 4.
    A. Krieg, in Modular Forms on the Half-Spaces of Quaternions, Lecture Notes in Mathematics, vol. 1143 (Springer, Berlin/Heidelberg/New York, 1985)Google Scholar
  5. 5.
    A. Krieg, The Maaß-Space on the Half-Space of Quaternions of Degree 2. Math. Ann. 276, 675–686 (1987)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Lehrstuhl A für MathematikAachenGermany

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