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On interaction of symplectic and orthogonal Hecke–Shimura rings of one-class quadratic forms

Transformation formulas of theta-series with harmonic polynomials of one-class quadratic forms under Hecke operators are interpreted as a result of interaction of the standard representation of the symplectic Hecke-Shimura ring on theta-series with the natural representation of the orthogonal Hecke-Shimura ring on the same theta-series considered as invariants of quadratic forms. Properties of the interaction rnaps and their relations to the action of Hecke operators are considered. Bibliography: 9 titles.

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Correspondence to A. N. Andrianov.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 5–17.

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Andrianov, A.N. On interaction of symplectic and orthogonal Hecke–Shimura rings of one-class quadratic forms. J Math Sci 193, 1–7 (2013). https://doi.org/10.1007/s10958-013-1428-0

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  • DOI: https://doi.org/10.1007/s10958-013-1428-0

Keywords

  • Quadratic Form
  • Standard Representation
  • Natural Representation
  • Transformation Formula
  • Harmonic Polynomial