The Restriction of Octonionic Theta Constants to the Quaternionic Half-Space

  • C. Dieckmann
  • A. KriegEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 115)


The paper describes the behaviour of octonionic theta constants under the restriction to the quaternionic half-space. As a result one can prove that the vector space, which is spanned by all restricted octonionic theta constants, coincides with the vector space spanned by quaternionic theta series of first respectively second kind.


Theta Constants Theta Series Vector Space Hurwitz Quaternions Maximum Order 
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The authors would like to thank the referee for valuable suggestions.


  1. 1.
    W.L. Baily, Introductory lectures on automorphic forms, Iwanami Shoten and Princeton (University Press, Tokyo-Princeton 1973)Google Scholar
  2. 2.
    H.-D. Ebbinghaus et al., Numbers (Springer, New York/Berlin/Heidelberg 1990)zbMATHGoogle Scholar
  3. 3.
    E. Freitag, C.F. Hermann, Some modular varieties of low dimension. Adv. Math. 152, 203–287 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    E. Freitag, R. Salvati Manni, Modular Forms for the Even Unimodular Lattice of Signature (2,10) (Heidelberg, 2005) PreprintGoogle Scholar
  5. 5.
    A. Krieg, Modular Forms on Half-Spaces of Quaternions, Lect. Notes Math. vol. 1143 (Springer, Berlin/Heidelberg/New York 1985)Google Scholar
  6. 6.
    A. Krieg, Theta series over the Hurwitz quaternions. Int. J. Number Theor. 6, 25–36 (2010)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Lehrstuhl A für MathematikRWTH AachenAachenGermany

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