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The Ramanujan Journal

, Volume 48, Issue 2, pp 385–398 | Cite as

The graded ring of modular forms on the Cayley half-space of degree two

  • C. Dieckmann
  • A. KriegEmail author
  • M. Woitalla
Article
  • 82 Downloads

Abstract

A result by Hashimoto and Ueda says that the graded ring of modular forms with respect to \({\mathrm{SO}}(2,10)\) is a polynomial ring in modular forms of weights 4, 10, 12, 16, 18, 22, 24, 28, 30, 36, 42. In this paper, we show that one may choose Eisenstein series as generators. This is done by calculating sufficiently many Fourier coefficients of the restrictions to the Hermitian half-space. Moreover, we give two constructions of the skew-symmetric modular form of weight 252.

Keywords

Modular forms Orthogonal group Cayley half-plane Graded ring Eisenstein series 

Mathematics Subject Classification

11F55 

Notes

Acknowledgements

The authors thank H. Hashimoto and T. Ueda for helpful discussions and in particular for pointing out the proof of Corollary 4.2 from [13].

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.RWTH Aachen UniversityAachenGermany

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